The pairwise comparison ratio scale that the Analytic Hierarchy Process (AHP) acquires a central role because it allows the incorporation of intangible information through expert judgments. Existing literature has been shown that preference results are sensitive to the scale used in ratio judgments. This paper applies the Intentional Bounded Rationality Methodology (IBRM) to study the performance of the most used AHP ratio scales in the literature. By adapting the AHP ratio scales to the IBRM, several scenarios are proposed based on the distribution of the latent performance of the alternatives for two different problems. In problem 1, it is assumed that the AHP comparison judgements are numerical and known to the expert, while in problem 2, the AHP comparison judgements are described linguistically without the expert being aware of their transformation into numerical values. Problem 1 is used to answer the following research question (1) which among a set of seven different ratio scales used in literature favor AHP expected performance?, while Problem 2 is used to answer the following research question (2) how much the expected performance in AHP deteriorates when the expert is only guided by verbal judgments? The expected performance of each of the considered ratio scales is obtained in each scenario for different levels of expertise of a decision-maker. For the first problem, the balanced scale and the power scale show the best and worst expected performances, respectively. Problem 2 compares these two scales and the results show their performance differences are below 8%, which is interpreted as a stability property of AHP with respect to scale changes. Finally, it is also shown that no matter which ratio scale is used, the requirement of the consistency property in AHP contributes positively to the expected performance.

Subjective probability distribution aggregation (SPDA) refers to the process of combining multiple expert judgments into a single representative distribution and has become essential for decision-making under deep uncertainty. Despite its importance, a systematic review of multiobjective optimization-driven approaches to SPDA remains lacking. To address this gap, we trace the paradigm evolution from classical axiomatic and Bayesian approaches to contemporary optimization-driven frameworks, revealing a progression from single-objective consensus maximization through biobjective consensus-confidence models to comprehensive multiobjective formulations incorporating fairness and social welfare. We conduct a systematic literature review and establish a unified taxonomy that classifies methods by structural objectives and behavioral tradeoffs. Bibliometric analysis reveals a marked shift toward socially informed aggregation, with fairness concern and group dynamics emerging as dominant themes. We systematically examine applications across risk engineering, economics and finance, climate science, and policy planning, demonstrating that method selection must align with domain-specific uncertainty structures. In addition, key research challenges are identified, and a forward-looking roadmap is outlined to guide future investigations. This synthesis consolidates existing advances and provides both theoretical foundations and practical guidance for developing next-generation SPDA methods that balance statistical performance with social acceptability in complex decision environments.

Traditional group decision making (GDM) problems typically aim to obtain a complete ranking of all considered alternatives from best to worst. However, in numerous real-life scenarios, there are instances where it is imperative to assign each alternative into one of two rank levels, creating a ranking where one subset of alternatives is prioritized above the other subset of alternatives. These scenarios are known as 2-rank GDM problems. While a range of methods exist for addressing 2-rank GDM problems, most are specifically tailored to multiattribute decision making situations, thereby limiting their applicability in scenarios involving preference relations. The linguistic preference relation (LPR) is an effective representation tool of decision makers’ (DMs’) preferences for pairwise comparisons of alternatives using linguistic terms. Since words may have different meanings for different DMs, a phenomenon known as personalized individual semantics (PISs), the modeling of linguistic PISs in 2-rank GDM problems with LPRs is worth investigating and challenging to address. Consequently, this article develops models to support consensus reaching for 2-rank linguistic GDM problems with PISs and consistency of DMs. Specifically, PIS consistency-driven models are initially employed to measure and improve the consistency of the LPRs of the individual DMs with unacceptable consistency level. Based on this foundation, the 2-rank vectors for both individuals and the group are determined. Subsequently, a 2-rank consensus measurement method is proposed on which a 2-rank consensus reaching process is designed to support DMs in improving their consensus levels. This involves the development of a PISs-based minimum adjustment consensus optimization model and a PISs-based individual consensus level maximization model. An algorithm to implement the proposed consensus reaching framework is also provided. Finally, numerical experiments and simulation results are reported to demonstrate the effectiveness of the proposed method.

In the consensus reaching process (CRP) of social network group decision making (SN-GDM), the non-cooperative behavior exhibited by experts will hinder the achievement of group consensus. This paper develops a non-cooperative behavior management framework based on trust propagation and dynamic cooperation index under bidirectional feedback context. On the one hand, a trust propagation operator with trust decay is established to enhance the trust relationship between non-cooperative experts; On the other hand, the fuzzy preference relations are utilized as preference expression structure, and the mutual reinforcing effect between consensus and trust is explored to achieve the dynamic enhancement of cooperation index, thereby facilitating the transformation of non-cooperative behavior. Specifically, a cooperation index is formulated to identify the non-cooperation behavior. Subsequently, a non-cooperative behavior transformation method by dynamic cooperation index is investigated. Finally, a bidirectional feedback mechanism is provided for group consensus reaching. This paper provides an innovative strategy for detecting and managing non-cooperative behavior, an illustrative example and some analyses are presented to verify the validity of proposed method.

In group decision-making (GDM), the opinions of decision-makers (DMs) are prone to having controversies and conflicts. Identifying individual personality traits can better predict the individual adjustment behavior of DMs in GDM and, therefore, construct the corresponding feedback strategies to guide opinion interaction and consensus building. To do that, large language models (LLMs) are utilized to analyze the individual Big Five personality traits revealed by online text information. Then, a conflict quadrant diagram (CQD) is developed to explore the conflict resolution behaviors manifested by DMs as influenced by their personality traits. Subsequently, a series of interaction rules corresponding to diverse conflict behaviors within the CQD are constructed, and then a personality traits-driven feedback model is proposed to generate personalized recommendation advice for group consensus interaction, with the overarching aim of effectively enhancing the level of group consensus. Finally, a simulation experiment on LLM-based agents is conducted to verify the opinion convergence process, and some sensitivity and comparative analyses are also provided. Overall, this article contributes to the innovative application of LLMs in solving GDM problems by prompt engineering to generate outputs and validate models and carries out in-depth explorations on integrating individual personality traits into the group consensus-building process.

Trust relationships can facilitate cooperation in collective decisions. Using behavioral incentives via trust to encourage voluntary preference adjustments improves consensus through mutual agreement. This article aims to establish a trust incentive-driven framework for enabling consensus in social network group decision making (SN-GDM). First, a trust incentive mechanism is modeled via interactive trust functions that integrate risk attitude. The inclusion of risk attitude is crucial as it reflects the diverse ways decision makers (DMs) respond to uncertainty in trusting others’ judgments, capturing the varied behaviors of risky, neutral, and insurance DMs in the consensus process. Inconsistent DMs then adjust opinions in exchange for heightened trust. This mechanism enhances the importance degrees via a new weight assignment method, serving as a reward to motivate DMs to further align with the majority. Subsequently, a trust incentive-driven bounded maximum consensus model is proposed to optimize cooperation dynamics while preventing over-compensation of adjustments. Simulations and comparative analysis demonstrate the model’s efficacy in facilitating cooperation through tailored trust incentive mechanisms that account for these diverse risk preferences. Finally, the approach is applied to evaluate candidates for the Norden Shipping Scholarship, providing a cooperation-focused SN-GDM framework for achieving mutually agreeable solutions while acknowledging the impact of individual risk attitude on trust-based interactions.

In green supply chain initiatives, small suppliers often struggle to achieve collaborative adjustment goals due to limited budgets, even when overall resources are sufficient. This reflects a common challenge in group decision making (GDM) under individual budget constraints. To address this, a novel framework is proposed for achieving group consensus in social networks with limited individual budgets. First, the minimum cost consensus model (MCCM) is extended by introducing a budget relaxation method to explore the potential of Pareto improvement when strict budget constraints hinder consensus. To realize this potential, an asymmetric Nash bargaining cost allocation model with compensation factors is developed to fairly distribute consensus costs within individual budgets. On this basis, an asymmetric Nash bargaining compensation mechanism in ego-networks is designed, reflecting the reality that in decentralized decision-making scenarios, compensation typically occurs among directly connected individuals due to stronger trust, more frequent interactions, and shared interests. This mechanism enables DM to negotiate and reallocate resources within their local social circles, balancing individual and collective benefits and enhancing the feasibility of cooperation. The effectiveness of the proposed framework is demonstrated through an illustrative example.

Abstract Quality management techniques such as the quality function deployment model can help hospitals assess and improve the quality of their services by integrating the voice of customers. The different quality parameters of this model are usually determined and assessed by experts; nonetheless, obtaining such experts is not always easy or inexpensive. Moreover, in this method, patient opinions are not usually considered directly, although they are the real users of the services and those who can best assess those services. Nevertheless, these opinions are easily accessible today, owing to the development of medical social networks where patients directly convey their opinions about the different services and features of a hospital. Therefore, it is feasible to replace expert knowledge with the information provided by these opinions. Based on this idea, this study proposes a novel fuzzy recommendation model based on the quality function deployment method to rank hospitals depending on patient opinions and preferences regarding hospital services. This model integrates a topic modeling strategy for determining hospital requirements, customer needs, and the relationship between them as well as a sentiment analysis algorithm for assessing customer satisfaction regarding hospital services. To demonstrate the usefulness of the proposed method, several experiments were conducted using patient reviews from real hospitals, and the method was compared against other recommendation models. The results prove that this approach represents a step toward more personalized and effective health care system selection considering patient preferences and opinions.

The manifestation of the intensity in the judgment of one alternative versus another in the peer comparison processes is a central element in some decision support techniques, such as the Analytical Hierarchy Process (AHP). However, its contribution regarding quality (expected performance) with respect to the priority vector has not been evaluated so far. Using the Intentional Bounded Rationality Methodology (IBRM), this work analyzes the gains obtained from requiring the decision-maker to report an intensity judgment in pairs (AHP) with respect to a technique that only requires expressing a preference (Ordering). The results show that when decision-makers have low levels of expertise, it is possible that a less informative and computational cheap technique (Ordering) performs better than a more informative and computational expensive one (AHP). When decision-makers have medium and high levels of expertise, AHP technique obtains modest gains with respect to the Ordering technique. This study proposes a cost-benefit analysis of decision support techniques contrasting the gains of a technique that requires more resources (AHP) against other that require less resources (Ordering). Our results can change the managing approach of the information obtained from experts’ judgments.

The use of social network to model the evolution of credit scores of networked enterprises is still a challenging task. This article develops an opinion dynamics model of the evolution of credit scores of enterprises in a social network. Firstly, based on the number of potential cooperated enterprises and the initial credit scores, the leader and follower enterprises are identified. Then, taking into consideration the cooperated benefit and discrimination cost, the cooperated utility between any two enterprises is calculated, which is used to compute the weights that one enterprise assigns to other enterprises. An opinion dynamics model on the evolution of credit scores of enterprises, inspired on the classical Friedkin–Johnsen’s social network model, is developed. Some desirable properties of the proposed opinion dynamics model are theoretically stated and proved. Finally, a numerical example is provided to illustrate the feasibility of the proposed opinion dynamics model, while a simulation analysis to investigate the joint influences of the connection probabilities and the network structure on the evolution of credit scores of enterprises is reported.

In traditional group decision making, the inconsistent experts are usually forced to make compromises toward the group opinion to increase the group consensus level. However, the strategy of reaching group consensus via an incentive mechanism encouraging adjustment of preferences is more effective than forcing, which is the aim of this article. Specifically, this article establishes a novel incentive mechanism to support group consensus under dynamic trust relationship. First, the supremum and infimum incentives-based rule driven by trust relationship is defined. Based on the assumption that if incentive conditions are met, then experts will be willing to adjust their preferences, the incentive behavior-driven minimum adjustment consensus model is developed to generate optimal incentive-based recommendation preferences. Thus, the proposed incentive mechanism can effectively reduce the preference adjustment cost and promote group consensus reaching. Third, the updated trust relationships between experts are shown to be strengthen by the proposed incentive-driven preference revision. Consequently, the optimization model based on trust interaction relationship is constructed to obtain the final group preference matrix. Finally, a supplier selection case of high-end medical equipment is provided to illustrate the proposed method and show the rationality and advantages of the proposed methodology with both a sensitivity analysis and a comparison analysis.

With the development of social democracy, the public begin to participate in large-scale group decision making (LSGDM) events that have a significant impact on their personal interests. However, the participation of the public with insufficient expertise will cause much hesitancy in the evaluations of decision makers (DMs), which can be captured by intuitionistic fuzzy sets. Meanwhile, due to the increment in the number of DMs, the cost of consensus reaching processes (CRPs), which are utilized to help DMs reach a consensus, is getting higher and higher. In order to improve the efficiency of the CRP, this paper presents a confidence and conflict-based consensus reaching process (CC-CRP) for LSGDM events with intuitionistic fuzzy representations. In the proposed model, according to the hesitancy of the DMs’ intuitionistic fuzzy evaluations, an objective method is firstly developed to calculate the confidence level of DMs that does not require any extra information. Then, a three-dimension clustering method is designed by considering the type of conflict, the degree of conflict, and the confidence level of DMs. After this, an efficiency rate of modification is defined to select DMs who will be persuaded first to adjust their evaluations with recommendation plans generated by a specific optimal method. Finally, according to the clustering process results, different CC-CRP management methods will apply to DMs with different attributes. An illustrative example and several experiments are reported to provide evidence that the proposed model is feasible and effective.

This article proposes a decayed trust propagation method among multiple overlapping communities, and establishes a trust-driven consensus model for social network group decision making (SN-GDM). On the one hand, the use of overlapping nodes simplifies trust propagation by bridging complex connections among multiply overlapping communities. On the other hand, trust models' accuracy and realism are enhanced with the concept of trust decay, which accounts for the temporal dynamics of trust propagation. Thus, a first objective of this paper is to develop a trust propagation operator based on trust decay among multiple overlapping communities by leveraging overlapping nodes. By incorporating overlapping nodes' diverse trust relationships and perspectives, this approach allows to achieve reliable sources for generating recommendations in SN-GDM. A second objective of this paper is to design a decayed trust propagation induced consensus model to determine the optimal combination of overlapping nodes and feedback parameters, while balancing consensus efficiency and interaction willingness. The innovation of this approach is grounded in its ability to avoid excessive group adjustment to reach consensus. Numerical examples and comparative analysis demonstrate the model's performance in achieving efficient consensus under various representative recommendations.

Failure modes and effect analysis (FMEA) is a promising reliability management approach widely used to prioritize the failure modes. Different backgrounds and levels of knowledge of FMEA participants may lead to substantial variation between their risk ratings, making the implementation of a consensus mechanism within FMEA to assist FMEA participants in reaching acceptable collective risk ratings worthwhile. Since social trust has an influence on individual's willingness to change risk ratings, this study discusses the role of social-trust-driven rating modifications willingness in prioritizing failure modes during the consensus reaching process. FMEA participants’ rejection of rating modifications suggestions significantly different from their trusted FMEA participants’ risk ratings is formulated as the basis assumption. Based on this assumption, a two-stage social-trust-driven consensus model is proposed to assist FMEA participants with linguistic distribution assessment in reaching consensus willingly. The proposed framework implements a social-trust-driven consensus model with a minimum number of rating modifications in its first stage and a social-trust-driven consensus model with a minimum distance of rating modifications in its second stage. A case study, related to the reliability management of automatic transmission of new energy vehicles, and a simulation analysis are presented and analyzed to validate the proposed FMEA approach.

Different from conventional decision-making environments, decision makers (DMs) in a community setting usually exhibit the complex social preferences and intricate social interactions, which may lead to high-decision costs for group consensus reaching. To address this challenge, we design a minimum cost consensus-based social network group decision making (SNGDM) approach considering altruism-fairness preferences and ordered trust propagation. First, a trust propagation method with order effect and path length is proposed to estimate the completed trust relationships among DMs in order to determine the weights of DMs. Then, inspired by the interaction of altruism and fairness preferences, we define the individual altruism-fairness preference utility function and utility level for cost consensus, and explore some properties. Afterwards, a new minimum cost consensus-based SNGDM with individual altruism-fairness preference utility is constructed. Finally, the validity of the proposed consensus framework is confirmed through the carbon reduction consensus problem of China’s aviation enterprises. Moreover, the sensitivity studies and comparative analysis are conducted to further demonstrate the merits of our proposal.

In social network group decision making (SN-GDM), overlapping communities are special community structures that can assist opinion interaction to reach group consensus. However, the specific mechanisms of how overlapping structures facilitate community interaction need to be further explored. In addition, the compromise behavior of decision makers (DMs) is conducive to group consensus, but it is usually fixed at the same value, and then it need further research the characteristic of the dynamics compromise limits. To this end, the overlapping community structures under DMs’ trust network is detected. Then, the effect of community overlap in social networks on community interaction is explored. Meanwhile, a limited compromise function is built based on prospect theory to describe the dynamic compromise behavior of communities. Hence, a dynamic compromise behavior driven bidirectional feedback mechanism with overlapping communities is proposed in the context of SN-GDM, and an illustrative example with comparative analysis is provided to testify the advantages of proposed method. It is proved that overlapping communities can improve the compromise willingness compared to nonoverlapping communities, indicating that overlapping communities can serve as a bridge to facilitate interaction, and the dynamic compromise behavior can more realistically describe the real behavior of DMs. In general terms, the proposed method provides a solution to the consensus reaching issue of SN-GDM from a new perspective. Specifically, it can be applied to real-life application scenarios, such as group recommendation to recommend acceptable solutions for social network group users.

The graph model is devoted to game conflicts arising from incongruent pursued objectives among conflicting parties. Considering that each conflicting party is composed of multiple individuals, preference conflicts stemming from differing cognitive levels and knowledge backgrounds exist among internal individuals. This scenario simultaneously involving game conflicts and preference conflicts is termed dual conflict decision-making problem. Tailored to effectively address this problem, this study proposes an enhanced graph model that incorporates internal consensus and external stability. The best-worst method, incorporating comparative linguistic expressions, is devised to effectively elicit individual preferences over game states. To mitigate preference conflicts inherent to internal individuals within conflicting party concerning game states, a consensus reaching model minimizing preference information loss is introduced. By this way, collective preferences are obtained. Based on these, the concept of “game consensus” is proposed to manage the game conflicts and the diverse behaviors exhibited by conflicting party. Finally, a case study regarding price conflict within a dual-channel supply chain, accompanied by a comparative analysis, is presented to validate the effectiveness of the proposal. Compared to existing graph model, the proposal effectively grapples with consensus issues and heterogeneous behaviors within conflicting parties, making it more valuable in practice.

Every decision may involve risks. Real-world risk issues are usually supervised by third parties. Decision-making may be affected by the absence of sufficient or reasonable trust or to the opposite, an unconditional, excessive, or blind trust, which is called trust risks. The conflict-eliminating process (CEP) aims to facilitate satisfactory consensus by decision makers (DMs) through continuous reconciliation between their opinion differences on the subject matter. This article addresses trust risks in CEP of social network group decision making (SNGDM) through third-party monitoring. A trust risk analysis-based conflict-eliminating model for SNGDM is developed. It is assumed that a third-party agency monitors the DMs' credibility and performance, which is recorded in an objective evaluation matrix and multi-attribute trust assessment matrix (MTAM). A trust risk measurement methodology is proposed to classify the DMs' different trust risk types and to measure the trust risk index (TRI) of a group of DMs. When TRI is unacceptable, a trust risk management mechanism that controls TRI is activated. Different management policies are applicable to DMs' different trust risk types. There are two main methods: 1) dynamically update the MTAM based on DMs' performance and 2) provide suggestions for modifying the DM's information with high TRI. Besides, as part of the integrated CEP, this model includes an optimization approach to dynamically derive DMs' reliable aggregation weights from their MTAM. Simulation experiments and an illustrative example support the feasibility and validity of the proposed model for managing trust risks in CEP of SNGDM.

This study proposes a minimum cost consensus-based failure mode and effect analysis (MCC-FMEA) framework considering experts' limited compromise and tolerance behaviors, where the first behavior indicates that a failure mode and effect analysis (FMEA) expert might not tolerate modifying his/her risk assessment without limitations, and the second behavior indicates that an FMEA expert will accept risk assessment suggestions without being paid for any cost if the suggested risk assessments fall within his/her tolerance threshold. First, an MCC-FMEA with limited compromise behaviors is presented. Second, experts' tolerance behaviors are added to the MCC-FMEA with limited compromise behaviors. Theoretical results indicate that in some cases, this MCC-FMEA with limited compromise and tolerance behaviors has no solution. Thus, a minimum compromise adjustment consensus model and a maximum consensus model with limited compromise behaviors are developed and analyzed, and an interactive MCC-FMEA framework, resulting in an FMEA problem consensual collective solution, is designed. A case study, regarding the assessment of COVID-19-related risk in radiation oncology, and a detailed sensitivity and comparative analysis with the existing FMEA approaches are provided to verify the effectiveness of the proposed approach to FMEA consensus-reaching.

Social network group decision-making (SN-GDM) provides valuable support for obtaining agreed decision results by effectively utilizing the connected social trust relationships among individuals. However, the impact of intricately overlapped social trust relationships within overlapping communities on evaluation modifications in the SN-GDM consensus reaching process is seldom considered. To alleviate this issue, this study attempts to construct an overlapping community driven feedback mechanism for improving consensus in SN-GDM. The Lancichinetti-Fortunato method (LFM) is used to detect the overlapping community structures under social trust networks. Subsequently, the trusted recommendation advice is conducted within overlapping communities, which guides the inconsistent subgroups to make an interaction with each other to reach higher consensus level. Then, an associated feedback mechanism for SN-GDM with overlapping communities is proposed, which enables the inconsistent subgroups to minimize the consensus cost by selecting personalized feedback parameters. Moreover, it shows that the overlapping communities based feedback mechanism is superior to the feedback mechanisms with non-overlapping communities. Finally, an illustrative example is included, which is also used to testify the efficacy of proposal by comparing the consensus cost under different representative recommendation advice in overlapping social trust networks.

This article proposes a novel framework to manage subgroups' noncooperative behavior by weight penalty in large-scale group decision making. To do that, a trust-consensus index (TCI) is defined by combining trust score and consensus degree among experts expressed by unbalanced linguistic term sets. A Louvain algorithm clustering process based on undirected graph composed of TCI is introduced to detect the subgroups in large network. Hence, a weight penalty feedback model is established to manage the subgroups detected as discordant and noncooperative. The proposed method novelty resides in that the minimum adjustment cost can be obtained with respect to the penalty parameter. A detail analysis regarding the computation of the optimal penalty parameter to prevent excessive penalization is reported. Finally, a detailed numerical and comparative analyses are provided to verify the validity of the proposed method.

The generation of collective opinion based on probability distribution function (PDF) aggregation is gradually becoming a critical approach for tackling immense and delicate assessment and evaluation tasks in decision analysis. However, the existing collective opinion generation approaches fail to model the behavioral characteristics associated with individuals, and thus, cannot reflect the fairness concerns among them when they consciously or unconsciously incorporate their judgments on the fairness level of distribution into the formulations of individual opinions. In this study, we propose a multiobjective optimization-driven collective opinion generation approach that generalizes the bi-objective optimization-based PDF aggregation paradigm. In doing so, we adapt the notion of fairness concern utility function to characterize the influence of fairness inclusion and take its maximization as an additional objective, together with the criteria of consensus and confidence levels, to achieve in generating collective opinion. The formulation of fairness concern is then transformed into the congregation of individual fairness concern utilities in the use of aggregation functions. We regard the generalized extended Bonferroni mean (BM) as an elaborated framework for aggregating individual fairness concern utilities. In such way, we establish the concept of BM-type collective fairness concern utility to empower multiobjective optimization-driven collective opinion generation approach with the capacity of modeling different structures associated with the expert group with fairness concern. The application of the proposed fairness-aware framework in the maturity assessment of building information modeling demonstrates the effectiveness and efficiency of multiobjective optimization-driven approach for generating collective opinion when accomplishing complicated assessment and evaluation tasks with data scarcity.

Preferences that verify the transitivity property are usually referred to as rational or consistent preferences. Existent methods to improve the consistency of inconsistent fuzzy reciprocal preference relations (FPRs) fail to retain the original preference values because they always derive a new FPR. This article presents a new inconsistency identification and modification (IIM) method to detect and rectify only the most inconsistent elements of an inconsistent FPR. As such, the proposed IIM can be considered a local adjustment method to improve multiplicative consistency (MC) of FPRs. The case of inconsistent FPRs with missing values, i.e., incomplete FPRs, is addressed with the estimation of the missing preferences with a constrained nonlinear optimization model by the application of the IIM method. The implementation process of the proposed algorithms is illustrated with numerical examples. Simulation experiments and comparisons with existent methods are also included to show that the new method requires fewer iterations than existent methods to improve the MC of FPRs and achieves better MC level, while preserving the original preference information as much as possible than the existent methods. Thus, the results presented in this article demonstrate the correctness, effectiveness, and robustness of the proposed method.

Successful new product development advocates for collaboration among different institutions in which technology transfer dispute widely exists. Although several studies have discussed conflict modeling and resolution in technology transfer disputes, scant research attempted to model third-party (or mediator) mediation, let alone develop effective approaches to minimize cost in the conflict resolution process. This study uses a graph model and minimum cost to investigate the conflict resolution and mediation in the technology transfer dispute of new product collaborative development. On the one hand, the conflict in technology transfer of new product collaborative development is modeled using the graph model theory, in which the stakeholders (or decision makers), their options, the feasible states, and the preferences of decision makers are analyzed. On the other hand, an inverse graph model with minimum cost is designed to tackle the problem of specifying which decision-makers’ preferences lead to a desired solution, thereby making it easier for a mediator or other third party to influence the course of the conflict. In the inverse graph model with minimum cost, two 0–1 mixed linear approaches are constructed to judge the Nash and general merataionality stabilities within the graph model, and several optimization-based models that minimize mediation cost are designed for the mediator to guide the technology transfer conflict resolution process to achieve the desired solution. Finally, the proposed methodology is applied to a technology transfer dispute case study.

Trust relation, as defined in Social Network Analysis (SNA), is one of the recent notions considered in decision making. This inspired our integration of trust relation in constructing a similarity–trust network. Similarity of experts' preferences is analyzed inclusively with trust relation by defining a new combination function of both attributes. The agglomerative hierarchical clustering approach is applied to group experts into subclusters based on the constructed similarity—trust degrees. The centrality concept from SNA is then used to determine the expert's similarity–trust centrality (STC) index, which is the basis for the construction of a new aggregation operator, STC-induced ordered weighted averaging operator, to fuse the individual experts' preferences into a collective one, from which the consensus solution is derived. An analysis of results with different levels of trust degree is carried out. We show that this new idea is promising and relevant to be used in solving certain consensus group decision-making problems.

Computational Intelligence (CI), originally represented by the three subjects of Evolutionary Computation (EC), Fuzzy Logic (FL) and Neural Networks (NNs), has significantly evolved to date and is ever more embedded in both software platforms and hardware devices forming intelligent systems capable of self-adaptation, decision-making and problem-solving.With a quick inspection of the scientific literature in Computer Science, one can indeed notice a significant expansion in the range of available CI tools, with, for example, modern EC optimisers making use of surrogate models (which can be based on NNs), or being used to evolve both topology and hyperparameters of neural systems.The latter systems have also grown significantly and currently offer numerous kinds of networks from, for example, recurrent, through convolutional to Generative/Adversarial deep NNs.These highly interconnected and high-level algorithms are becoming ubiquitous as their applicability has widened and grown to traverse many disciplines and application domains.In the past, the technological fields that benefited the most from applying CI techniques were in engineering, such as system control and design, robotics, telecommunication and so forth.However, the application scope of modern CI methods has widened significantly, thus making it possible to analyse large data sets, manipulate images and videos, extract sentiment and relevant information from plain text and audio recordings.Hence, modern CI turns out to be helpful in many areas which strongly impact our society, for example, medicine, finance, education, intelligent transportation, sustainability and so forth, where it is key to analyse available data, optimise processes and provide systems with extra capabilities.If placed in the right context, CI has then the potential of generating societal impact beyond enabling technological advancement per se.It can now support the deployment of technology to optimise not only the financial viability but as well the usability and benefit to the public.State-of-the-art optimisation has become focused on sustainability and waste rather than profit or cost reduction; now optimisation is critical to address the compromise between protecting society and the economic activities of small stockholders, and not just the large scale businesses.In this light, this special issue has gathered recent advances in CI addressing relevant research questions leading to societal impact and calling for the design of more intelligent systems enhancing our society in the future.

The unfolding coronavirus (COVID-19) pandemic has highlighted the global need for robust predictive and containment tools and strategies. COVID-19 continues to cause widespread economic and social turmoil, and while the current focus is on both minimising the spread of the disease and deploying a range of vaccines to save lives, attention will soon turn to future proofing. In line with this, this paper proposes a prediction and containment model that could be used for pandemics and natural disasters. It combines selective lockdowns and protective cordons to rapidly contain the hazard while allowing minimally impacted local communities to conduct "business as usual" and/or offer support to highly impacted areas. A flexible, easy to use data analytics model, based on Self Organising Maps, is developed to facilitate easy decision making by governments and organisations. Comparative tests using publicly available data for Great Britain (GB) show that through the use of the proposed prediction and containment strategy, it is possible to reduce the peak infection rate, while keeping several regions (up to 25% of GB parliamentary constituencies) economically active within protective cordons.

Building green airports can be regarded as among the most promising routes to sustainable development of ecosystems and human health. This study aims at addressing the problem of green airport plan selection under an uncertain context by developing an uncertain multiattribute group decision making (MAGDM) model. In the proposed model, the assessment information is characterized in the form of a proportional hesitant 2-tuple linguistic term set (PH2TLTS), which incorporates in binary form linguistic information that can accurately quantify subjective assessment information provided under uncertainty. The weights of assessment attributes of green airport plans are obtained automatically through a nonlinear programming model, which enhances the robustness of the decision-making method. Subsequently, on the basis of PH2TLTSs, three distance measures are proposed: the proportional hesitant 2-tuple linguistic Jaccard distance (PH2TLJD), the supplementary proportional hesitant 2-tuple linguistic normalized Minkowski distance (SPH2TLNMD) and the cluster-based proportional hesitant 2-tuple linguistic normalized Minkowski distance (CBPH2TLNMD). The TOPSIS-based comparison method proposed here can better determine the priorities of PH2TLTSs. The ranking and selection of green airport plans are derived using the PH2TL-VIKOR model. Finally, a case study accompanied by sensitivity and comparative analyses is performed to verify the rationality and feasibility of the proposed model.

In linguistic decision-making problems, there may be cases when decision makers will not be able to provide complete linguistic preference relations. However, when estimating unknown linguistic preference values in incomplete preference relations, the existing research approaches ignore the fact that words mean different things for different people, that is, decision makers have personalized individual semantics (PISs) regarding words. To manage incomplete linguistic preference relations with PISs, in this article, we propose a consistency-driven methodology both to estimate the incomplete linguistic preference values and to obtain the personalized numerical meanings of linguistic values of the different decision makers. The proposed incomplete linguistic preference estimation method combines the characteristic of the personalized representation of decision makers and guarantees the optimum consistency of incomplete linguistic preference relations in the implementation process. Numerical examples and a comparative analysis are included to justify the feasibility of the PISs-based incomplete linguistic preference estimation method.

Consistency is an important issue in linguistic decision making with various consistency measures and consistency improving methods available in the literature. However, existing linguistic consistency studies omit the fact that words mean different things for different people, that is, decision makers' personalized individual semantics (PISs) over their expressed linguistic preferences are ignored. Therefore, the aim of this article is to propose a novel consistency improving approach based on PISs in linguistic group decision making. The proposed approach combines the characteristics of personalized representation and integrates the PIS-based model in measuring and improving the consistency of linguistic preference relations. A detailed numerical and comparative analysis to support the feasibility of the proposed approach is provided.

A two-fold personalized feedback mechanism is established for consensus reaching in social network group decision-making (SN-GDM). It consists of two stages: 1) generating the trusted recommendation advice for individuals and 2) producing a a personalized adoption coefficient for reducing unnecessary adjustment costs. A uninorm interval-valued trust propagation operator is developed to obtain an indirect trust relationship, which is used to generate personalized recommendation advice based on the principle of "a recommendation being more acceptable the higher the level of trust it derives from." An optimization model is built to minimize the total adjustment cost of reaching consensus by determining the personalized feedback adoption coefficient based on individuals' consensus levels. Consequently, the proposed two-fold personalized feedback mechanism achieves a balance between group consensus and individual personality. An example to demonstrate how the proposed two-fold personalized feedback mechanism works is included, which is also used to show its rationality by comparing it with the traditional feedback mechanism in group decision making (GDM).

Inspired by the continuous opinion and discrete action (CODA) model, bounded confidence and social networks, the bounded confidence evolution of opinions and actions in social networks is investigated and a social network opinions and actions evolutions (SNOAEs) model is proposed. In the SNOAE model, it is assumed that each agent has a CODA for a certain issue. Agents' opinions are private and invisible, that is, an individual agent only knows its own opinion and cannot obtain other agents' opinions unless there is a social network connection edge that allows their communication; agents' actions are public and visible to all agents and impact other agents' actions. Opinions and actions evolve in a directed social network. In the limitation of the bounded confidence, other agents' actions or agents' opinions noticed or obtained by network communication, respectively, are used by agents to update their opinions. Based on the SNOAE model, the evolution of the opinions and actions with bounded confidence is investigated in social networks both theoretically and experimentally with a detailed simulation analysis. Theoretical research results show that discrete actions can attract agents who trust the discrete action, and make agents to express extreme opinions. Simulation experiments results show that social network connection probability, bounded confidence, and the opinion threshold of action choice parameters have strong impacts on the evolution of opinions and actions. However, the number of agents in the social network has no obvious influence on the evolution of opinions and actions.

Consensus reaching process (CRP) is important and present in a wide range of application areas. In practical CRP, the managers (e.g., enterprise) often hire some informed individuals (e.g., persuaders) to promote the efficiency of consensus reaching. This article proposes a CRP with minimum cost of informed individuals and time constraint in large-scale group decision-making (LSGDM) with bounded confidence effects. The consensus model with bounded confidence effects (CBC model) is formulated. Then, desirable properties of the CBC model are discussed to facilitate its resolution. Next, an extended particle swarm optimization algorithm is designed to solve the CBC model. Finally, a numerical analysis, a comparison analysis, and a simulation analysis are provided to illustrate the feasibility and effectiveness of the proposed approach.

This article presents a theoretical framework for a dynamic feedback mechanism in group decision making (GDM) by the implementation of an attitudinal consensus threshold (ACT) to generate recommendation advice for the identified inconsistent experts with the aim to increase consensus. The novelty of the approach resides in its ability to implement the ACT continuously, which allows the covering of all possible consensus states of the group from its minimum to maximum consensus degrees. Therefore, it can be flexibly applied to GDM problems with different consistency requirements. A sensitivity analysis method with visual simulation is proposed to support the checking of the numbers of experts involved in the feedback process and the minimum adjustment cost associated with the different ACT intervals. Experimental results show that an increase in the ACT value will lead to an increase in the number of experts and adjustment cost involved in the feedback process. Eventually, a numerical example is included to simulate the feedback process under various decision making scenarios with different ACT intervals.

This article investigates a two-stage consensus feedback mechanism that considers different power structures in large-scale group decision-making (LSGDM) environments. A Louvain algorithm type is used to detect subgroups in LSGDM by trust relationship. The concepts of internal subgroups and external subgroup consensus levels are defined, and an approach to identify the inconsistent individual/subgroup is developed to avoid the issue of “pseudoconsensus.” Combined with the background of the company’s shareholder power management regulations, the following three power structures are constructed: “absolute power,” “relative power,” and “democratic power.” A two-stage feedback mechanism is investigated with minimum adjustments to achieve the optimal power allocation under each power structure. This mechanism supports individuals reach consensus both inside and outside their subgroup. An illustrative example and discussions to verify the validity of the proposed method are reported.

Existing consensus models focus on improving the group consensus level, but ignore whether a higher group consensus level means higher mutual acceptance of decision makers. In the field of opinion dynamics, the bounded confidence model asserts that the decision makers will accept the preferences of others within a neighborhood of theirs with width a certain confidence level. Inspired by this research methodology, this article develops a consensus model to address the acceptance issue based on individual bounded confidences. Specifically, a bounded confidence-based consensus measure is designed to measure the level of group mutual acceptance, and a multi-stage optimization feedback mechanism based on individual bounded confidences is proposed to maximize the group mutual acceptance and minimize the amount of preference adjustment. A numerical example and a simulation analysis are included to illustrate the use of the model and to justify its effectiveness, respectively.

Social network group decision making (SNGDM) has emerged as a new decision tool to effectively model the social trust relationships among decision makers. The impact of the social trust relationships on assessments-modifications in the consensus reaching in the SNGDM is seldom considered. This study aims at addressing this issue. The main starting point is the assumption that a decision maker will not be willing to accept the assessments-modifications suggestions that significantly differ from his/her trusted decision makers’ assessments in a social trust network. Thus, this study proposes a social trust driven minimum adjustments consensus model (STDMACM) for SNGDM. Simultaneously, a social trust driven consensus maximum optimization model (STDCMOM) is proposed for maximizing the consensus level among decision makers under the above assumption. Based on both STDCMOM and STDMACM, an interactive consensus reaching process is presented, in which the assessments-modifications suggestions generated from the STDMACM are used, when the maximum consensus level obtained from STDCMOM is acceptable, as the references for guiding the consensus reaching; otherwise, assessments-modifications suggestions are generated from the designed STDCMOM. The validity of the social trust driven consensus reaching process with respect to its consensus convergence rate and consensus success ratio is verified with a simulation and comparison analysis.

This article investigates multiplicative consistency ascertaining, inconsistency repairing, and weights derivation for hesitant multiplicative preference relations (HMPRs). First, the completely multiplicative consistency and weakly multiplicative consistency of HMPRs are defined. Based on them, 0–1 mixed programming models and simple algebraic operations are proposed to ascertain the multiplicative consistency of HMPRs. Then, some goal programming models are developed to generate the weights from consistent HMPRs and to revise inconsistent HMPRs. An integrated procedure to manage the multiplicative consistencies of HMPRs is designed. The proposed methods are also extended to accommodate incomplete HMPRs, and to estimate missing values. Finally, some numerical examples, a comparative analysis with existent approaches, and a simulation analysis are included to illustrate the practicality and effectiveness of the developed models.

In a Group Decision Making problem, several people try to reach a single common decision by selecting one of the possible alternatives according to their respective preferences. So, a consensus process is performed in order to increase the level of accord amongst people, called experts, before obtaining the final solution. Improving the consensus degree as much as possible is a very interesting task in the process. In the evaluation of the consensus degree, the measurement of the distance representing disagreement among the experts’ preferences should be considered. Different distance functions have been proposed to implement in consensus models. The Euclidean distance function is one of the most commonly used. This paper analyzes how to improve the consensus degrees, obtained through the Euclidean distance function, when the preferences of the experts are slightly modified by using one of the properties of the Uniform distribution. We fulfil an experimental study that shows the betterment in the consensus degrees when the Uniform extension is applied, taking into account different number of experts and alternatives.

Correlation is an important index in decision-making. In weighted extended hesitant fuzzy sets (WEHFSs) environment, researchers have only defined a class of correlation coefficients between WEHFSs with values in the unit interval [ 0 , 1 ] . This is not ideal because it does not extend the classical correlation coefficient in the case of classical sets. In fact, the negative values of the interval [ − 1 , 1 ] are ignored, and such neglectfulness leads to unreasonable results in decision-making. In other words, the existing definitions are unconvincing and lack consistency, which hinder their application potentials. This article addresses this issue by introducing a new class of weighted correlation coefficients of WEHFSs with values in the interval [ − 1 , 1 ] . Three decision-making methodologies based on the weighted correlation coefficients of WEHFSs are compared with the existing methodologies based on their respective correlation coefficients in the unit interval [ 0 , 1 ] . The comparative analysis shows both the efficiency and effectiveness of the new correlation index.

One worthwhile way of expressing imprecise information is the q-rung orthopair fuzzy sets (q-ROFSs), which extend intuitionistic fuzzy sets and Pythagorean fuzzy sets. The main goal of this contribution is to further extend the concept of similarity measure for q-ROFSs, which not only endows the similarity framework with more ability to create new ones but also inherits all essential properties of a logical similarity measure. This contribution proposes a class of novel similarity measures for q-ROFSs by drawing a general framework of existing q-ROFS similarity and q-ROFS distance measures. These q-ROFS similarity measures enable us to overcome the theoretical drawbacks of the existing measures in the case where they are used individually. In the application part of the contribution, a pattern recognition problem on classification of building materials with a number of known building materials is reconsidered. The study of this particular case shows that the proposed family of similarity measures consistently classify the unknown building material pattern with the same known building material pattern. Then, an experimental case study regarding a problem of classroom teaching quality is re-examined for the comparison of the performance of proposed similarity measures against the existing ones. The salient features of the proposed similarity measures in comparison to the existing qROFS similarity measures, are as follows: (i) a number of existing q-ROFS similarity measures are inherently correlation coefficients, and they satisfy only a limited number of essential properties of a comprehensive similarity measure; (ii) several existing q-ROFS similarity measures lead sometimes to nonlogical results, more specifically, to the same maximum similarity value for different q-ROFSs; (iii) a variety of existing q-ROFS similarity measures depend on subjective parameters, which either hinder their application in practice or increase their computational cost. In brief, following this direction of research, we will prove the superiority of the developed similarity measures over the existing ones from both theoretical and experimental viewpoints.

With the development of the information and Internet technology, the public opinions with big data will rapidly emerge in an online-offline social network, and an inefficient management of public opinions often will lead to the security crisis for either firms or governments. To unveil the interaction mechanism among a large number of agents between the online and offline social networks, in this paper we propose the public opinion dynamics model in an online-offline social network context. Next, in the theory aspect we investigate the analytical conditions to form a consensus in the public opinion dynamics model. Furthermore, we conduct the extensive simulations to investigate how the online agents impact the dynamics of public opinion formation, and unfold that the online agents shorten the steady-state time, decrease the number of opinion clusters, and smoothen the opinion changes in the opinion dynamics. The increase in the size of the online agents often enhances these effects. The results in this paper can provide a basis for the management of the public opinions in the Internet age.

In this article, a novel framework to prevent manipulation behavior in consensus reaching process under social network group decision making is proposed, which is based on a theoretically sound optimal feedback model. The manipulation behavior classification is twofold: first, “individual manipulation” where each expert manipulates his/her own behavior to achieve higher importance degree (weight); and second, “group manipulation” where a group of experts force inconsistent experts to adopt specific recommendation advices obtained via the use of a fixed feedback parameter. To counteract “individual manipulation,” a behavioral weights assignment method modeling sequential attitude ranging from “dictatorship” to “democracy” is developed, and then a reasonable policy for group minimum adjustment cost is established to assign appropriate weights to experts. To prevent “group manipulation,” an optimal feedback model is investigated where objective function is the individual adjustments cost and constraints related to the group threshold of consensus. This approach allows the inconsistent experts to balance group consensus and adjustment cost, which enhances their willingness to adopt the recommendation advices and consequently the group reaching consensus on the decision-making problem at hand. A numerical example is presented to illustrate and verify the proposed optimal feedback model.

The type-1 ordered weighted averaging (T1OWA) operator has demonstrated the capacity for directly aggregating multiple sources of linguistic information modeled by fuzzy sets rather than crisp values. Yager's ordered weighted averaging (OWA) operators possess the properties of idempotence, monotonicity, compensativeness, and commutativity. This article aims to address whether or not T1OWA operators possess these properties when the inputs and associated weights are fuzzy sets instead of crisp numbers. To this end, a partially ordered relation of fuzzy sets is defined based on the fuzzy maximum (join) and fuzzy minimum (meet) operators of fuzzy sets, and an alpha-equivalently-ordered relation of groups of fuzzy sets is proposed. Moreover, as the extension of orness and andness of an Yager's OWA operator, joinness and meetness of a T1OWA operator are formalized, respectively. Then, based on these concepts and the representation theorem of T1OWA operators, we prove that T1OWA operators hold the same properties as Yager's OWA operators possess, i.e., idempotence, monotonicity, compensativeness, and commutativity. Various numerical examples and a case study of diabetes diagnosis are provided to validate the theoretical analyses of these properties in aggregating multiple sources of uncertain information and improving integrated diagnosis, respectively.

This article proposes a framework of personalized feedback mechanism to help multiple inconsistent experts to reach consensus in group decision making by allowing to select different feedback parameters according to individual consensus degree. The general harmony degree (GHD) is defined to determine the before/after feedback difference between the original and revised opinions. It is proved that the GHD index is monotonically decreasing with respect to the feedback parameter, which means that higher parameter values will result in higher changes of opinions. An optimization model is built with the GHD as the objective function and the consensus thresholds as constraints, with the solution being personalized feedback advices to the inconsistent experts that keep a balance between consensus (group aim) and independence (individual aim). This approach is, therefore, more reasonable than the unpersonalized feedback mechanisms in which the inconsistent experts are forced to adopt feedback generated with only consensus target without considering the extent of the changes acceptable by individual experts. Furthermore, the following interesting theoretical results are also proved: 1) the personalized feedback mechanism guarantees that the increase of consensus level after feedback advices are implemented; 2) the GHD by the personalized feedback mechanism is higher than that of the unpersonalized one; and 3) the personalized feedback mechanism generalizes the unpersonalized one as it is proved the latter is a particular type of the former. Finally, a numerical example is provided to model the feedback process and to corroborates these results when comparing both feedback mechanism approaches.

This article provides a brief tour through the main fuzzy and linguistic decision-making trends, studies, methodologies, and models developed in the last 50 years. Fuzzy and linguistic decision-making approaches allow to address complex real-world decision problems where humans exhibit vagueness, imprecision, and/or use natural language to assess decision alternatives, criteria, etc. The aim of this article is threefold. First, the main fuzzy set theory and computing with words-based representation paradigms of decision information, with their different levels of expressive richness and complexity, are reviewed. Second, three core decision-making frameworks are examined: 1) multicriteria decision making; 2) group consensus-driven decision making; and 3) multiperson multicriteria decision making. Third, the article discusses new complex decision-making frameworks that have emerged in recent years, where decisions are guided by the “wisdom of the crowd”: their associated challenges are highlighted and considerations on much needed key guidelines for future research in the field are provided.

Consistency, multiplicative and ordinal, of fuzzy preference relations (FPRs) is investigated. The geometric consistency index (GCI) approximated thresholds are extended to measure the degree of consistency for an FPR. For inconsistent FPRs, two algorithms are devised: 1) to find the multiplicative inconsistent elements and 2) to detect the ordinally inconsistent elements. An integrated algorithm is proposed to improve simultaneously the ordinal and multiplicative consistencies. Finally, some examples, comparative analysis, and simulation experiments are provided to demonstrate the effectiveness of the proposed methods.

Different feedback mechanisms have been reported in consensus reaching models to provide advices for preference adjustment to assist decision makers to improve their consensus levels. However, most feedback mechanisms do not consider the willingness of decision makers to accept these advices. In the opinion dynamics discipline, the bounded confidence model justifies well that in the process of interaction a decision maker only considers the preferences that do not exceed a certain confidence level compared to his own preference. Inspired by this idea, this article proposes a new consensus reaching model with personalized feedback mechanism to help decision makers with bounded confidences in achieving consensus. Specifically, the personalized feedback mechanism produces more acceptable advices in the two cases where bounded confidences are known or unknown, and the unknown ones are estimated by a learning algorithm. Finally, numerical example and simulation analysis are presented to explore the effectiveness of the proposed model in reaching consensus.

In the bounded confidence model, it is widely known that individuals rely on the opinions of their close friends or people with similar interests. Meanwhile, the decision maker always hopes that the opinions of individuals can reach a consensus in a required time. Therefore, with this idea in mind, this article develops a consensus reaching model with time constraints and minimum adjustments in a group with bounded confidence effects. In the proposed consensus approach, the minimum adjustments rule is used to modify the initial opinions of individuals with bounded confidence, which can further influence the opinion evolutions of individuals to reach a consensus in a required time. The properties of the model are studied, and detailed numerical examples and comparative simulation analysis are provided to justify its feasibility.

The ability for grocery retailers to have a single view of customers across all their grocery purchases remains elusive and has become increasingly important in recent years (especially in the United Kingdom) where competition has intensified, shopping habits and demographics have changed and price sensitivity has increased following the 2008 recession. Numerous studies have been conducted on understanding independent items that are frequently bought together (association rule mining/frequent itemsets) with several measures proposed to aggregate item support and rule confidence with varying levels of accuracy as these measures are highly context dependent. Uninorms were used as an alternative measure to aggregate support and confidence in analysing market basket data using the UK grocery retail sector as a case study. Experiments were conducted on consumer panel data with the aim of comparing the uninorm against three other popular measures (Jaccard, Cosine and Conviction). It was found that the uninorm outperformed other models on its adherence to the fundamental monotonicity property of support in market basket analysis (MBA). Future work will include the extension of this analysis to provide a generalised model for market basket analysis.

Nowadays, in the social network–based decision-making processes, like the ones involved in e-commerce and e-democracy, multiple users with different backgrounds may take part and diverse alternatives might be involved. This diversity enriches the process, but at the same time, increases the uncertainty of opinions. This uncertainty can be considered from two different perspectives: (i) the uncertainty in the meaning of the words given as preferences, that is, motivated by the heterogeneity of the decision makers; and (ii) the uncertainty inherent to any decision-making process that may lead to an expert not being able to provide all their judgments. The main objective of this study is to address these two types of uncertainty. To do so, the following approaches are proposed: First, to capture, process, and keep the uncertainty in the meaning of the linguistic assumption, the Interval Type-2 Fuzzy Sets are introduced as a way to model the experts' linguistic judgments. Second, a measure of the coherence of the information provided by each decision maker is proposed. Finally, a consistency-based completion approach is introduced to deal with the uncertainty presented in the expert judgments. The proposed approach is tested in an e-democracy decision-making scenario.

On-line platforms foster the communication capabilities of the Internet to develop large-scale influence networks in which the quality of the interactions can be evaluated based on trust and reputation. So far, this technology is well known for building trust and harnessing cooperation in on-line marketplaces, such as Amazon (www.amazon.com) and eBay (www.ebay.es). However, these mechanisms are poised to have a broader impact on a wide range of scenarios, from large scale decision making procedures, such as the ones implied in e-democracy, to trust based recommendations on e-health context or influence and performance assessment in e-marketing and e-learning systems. This contribution surveys the progress in understanding the new possibilities and challenges that trust and reputation systems pose. To do so, it discusses trust, reputation and influence which are important measures in networked based communication mechanisms to support the worthiness of information, products, services opinions and recommendations. The existent mechanisms to estimate and propagate trust and reputation, in distributed networked scenarios, and how these measures can be integrated in decision making to reach consensus among the agents are analysed. Furthermore, it also provides an overview of the relevant work in opinion dynamics and influence assessment, as part of social networks. Finally, it identifies challenges and research opportunities on how the so called trust based network can be leveraged as an influence measure to foster decision making processes and recommendation mechanisms in complex social networks scenarios with uncertain knowledge, like the mentioned in e-health and e-marketing frameworks.

This paper puts forward a trust-based framework for building a recommendation mechanism for consensus in group decision making with interval-valued intuitionistic fuzzy information. It first presents an attitudinal trust model where experts assign trust weights to others considering the concept of attitude of the group. This approach allows for the implementation of the group attitude in a continuous scale ranging from a pessimistic attitude to an indifferent attitude. Thus, it can express the continuous trust status, and consequently it generalizes the traditional simplified trust model: `trusting' and `distrusting.' In particular, three typical policies are defined as: `extreme trust policy,' `bounded trust policy,' and `indifferent trust policy.' Second, the attitudinal trust induced recommendation mechanism is established by a reasonable rule: the closer the experts, the higher their trust degree. This can guarantee that the consensus level of the inconsistent expert is increased after adopting the recommended advices. In addition to group consensus, experts envisage to keep their original opinions as much as possible. A harmony degree (HD) is defined to determine the extent of the difference between an original opinion and the corresponding revised opinion after adopting the recommended advices. Combining the HD index and the consensus index, a sensitivity analysis with attitudinal parameter is proposed to verify the rationality of the proposed attitudinal trust recommendation mechanism. In practice, this will facilitate the inconsistent experts to achieve a balance between consensus degree and HD by selecting an appropriate attitudinal parameter.

In multiple attribute decision making (MADM), strategic weight manipulation is understood as a deliberate manipulation of attribute weight setting to achieve a desired ranking of alternatives. In this paper, we study the strategic weight manipulation in a group decision making (GDM) context with interval attribute weight information. In GDM, the revision of the decision makers' original attribute weight information implies a cost. Driven by a desire to minimize the cost, we propose the minimum cost strategic weight manipulation model, which is achieved via optimization approach, with the mixed 0-1 linear programming model being proved appropriate in this context. Meanwhile, some desired properties to manipulate a strategic attribute weight based on the ranking range under interval attribute weight information are proposed. Finally, numerical analysis and simulation experiments are provided with a twofold aim: 1) to verify the validity of the proposed models and 2) to show the effects of interval attribute weights information and the unit cost, respectively, on the cost to manipulate strategic weights in the MADM in a group decision context.

Large-scale group decision making (LGDM) is becoming more and more common, and how to assure the security and quality of the decision process has become a hot topic. Supply chain risk mitigation is a LGDM problem which involves many stakeholders. In the decision making process, a group of experts aims at reaching a consensus among alternatives in which non-cooperative behaviors often appear. Some experts might designedly form a small alliance and change their preferences in a direction against consensus with the aim to foster the alliance's own interests. In this study, we present a novel large-scale consensus reaching framework based on a self-management mechanism to manage non-cooperative behaviors. In the proposed framework, experts are classified into different subgroups using a clustering method, and they provide their evaluation information, i.e., the multi-criteria mutual evaluation matrices (MCMEMs), regarding the obtained subgroups based on their performance. The subgroups' weights are generated dynamically from the MCMEMs, which are in turn used to update experts' weights. This self-management mechanism allows penalizing the weights of the experts with non-cooperative behaviors. Detailed comparison analysis is presented to verify the validity of the proposed consensus framework.

In group decision making problems, the soft consensus calculus is an important topic. Soft consensus measures are utilized to show the different agreement degrees between decisors. Using the concept of coincidence we have two main approaches to calculating soft consensus measures: concordance among expert preferences and concordance among individual solutions. In the first, the coincidence is obtained by evaluating the similarity among the expert preferences, while in the second one the concordance is derived from the measurement of the similarity among the solutions proposed by these decisors or experts. In this paper we perform a basic comparative study of consensus calculus based on both coincidence approaches. We use the nonparametric Wilcoxon signed-ranks test to compare these approaches. We obtain significant differences between both approaches for measuring consensus.

The age of the population in the developed countries is increasing as well as the life expectancy for this population. This suppose a challenge for the health care system that requires of new tools to be able to face the increasing expenses that this ageing in the population suppose. With this regard, it has been demonstrated that promoting physical activity in the elderly, could prevent functional decline, frailty, falls, and fractures and reduce the risk of premature mortality. However, in order to obtain the maximum benefits of this physical activity, the activity prescription and health coaching support requires to be tailored to the functional and personal characteristics of each individual [23]. Therefore, it is of vital relevance to have tools to asses the elderly physical condition in an easy way using low cost and simple tools. In this contribution we present a preliminary version of a mobile health application, m-health app, specially aimed for the elderly population. The proposed approach offers to the health practitioners a reliable, real-time, affordable and easy to use tool to evaluate senior patients physical condition. This m-Health System could be a promising approach not only for physical assessment but as well as a tool in intervention programs to asses the patient evolution.

In this paper, the Type-Reduced Set (TRS) of the continuous type-2 fuzzy set is considered as an object in its own right. The structures of the TRSs of both the interval and generalised forms of the type-2 fuzzy set are investigated. In each case the respective TRS structure is approached by first examining the TRS of the discretised set. The TRS of a continuous interval type-2 fuzzy set is demonstrated to be a continuous horizontal straight line, and that of a generalised type-2 fuzzy set, a continuous, convex curve. This analysis leads on to the concept of truncation, and the definition of the truncation grade. The truncated type-2 fuzzy set is then defined, whose TRS (and hence defuzzified value) is identical to that of the non-truncated type-2 fuzzy set. This result is termed the Type-2 Truncation Theorem, an immediate corollary of which is the Type-2 Equivalence Theorem which states that the defuzzified values of type-2 fuzzy sets that are equivalent under truncation are equal. Experimental corroboration of the equivalence of the non-truncated and truncated generalised type-2 fuzzy set is provided. The implications of these theorems for uncertainty quantification are explored. The theorem's repercussions for type-2 defuzzification employing the α-Planes Representation are examined; it is shown that the known inaccuracies of the α-Planes Method are deeply entrenched.

Although fuzzy preference relations (FPRs) are among the most commonly used preference models in group decision making (GDM), they are not free from drawbacks. First of all, especially when dealing with many alternatives, the definition of FPRs becomes complex and time consuming. Moreover, they allow to focus on only two options at a time. This facilitates the expression of preferences but let experts lose the global perception of the problem with the risk of introducing inconsistencies that impact negatively on the whole decision process. For these reasons, different preference models are often adopted in real GDM settings and, if necessary, transformation functions are applied to obtain equivalent FPRs. In this paper, we propose fuzzy rankings, a new approximate preference model that offers a higher level of user-friendliness with respect to FPRs while trying to maintain an adequate level of expressiveness. Fuzzy rankings allow experts to focus on two alternatives at a time without losing the global picture so reducing inconsistencies. Conversion algorithms from fuzzy rankings to FPRs and backward are defined as well as similarity measures, useful when evaluating the concordance between experts’ opinion. A comparison of the proposed model with related works is reported as well as several explicative examples.

In decision making, a widely used methodology to manage unbalanced fuzzy linguistic information is the linguistic hierarchy (LH), which relies on a linguistic symbolic computational model based on ordinal 2-tuple linguistic representation. However, the ordinal 2-tuple linguistic approach does not exploit all advantages of Zadeh's fuzzy linguistic approach to model uncertainty because the membership function shapes are ignored. Furthermore, the LH methodology is an indirect approach that relies on the uniform distribution of symmetric linguistic assessments. These drawbacks are overcome by applying a fuzzy methodology based on the implementation of the type-1 ordered weighted average (T1OWA) operator. The T1OWA operator is not a symbolic operator and it allows to directly aggregate membership functions, which in practice means that the T1OWA methodology is suitable for both balanced and unbalanced linguistic contexts and with heterogeneous membership functions. Furthermore, the final output of the T1OWA methodology is always fuzzy and defined in the same domain of the original unbalanced fuzzy linguistic labels, which facilitates its interpretation via a visual joint representation. A case study is presented where the T1OWA operator methodology is used to assess the creditworthiness of European bonds based on real credit risk ratings of individual Eurozone member states modeled as unbalanced fuzzy linguistic labels.

Decision situations in which several individual are involved are known as group decision-making (GDM) problems. In such problems, each member of the group, recognizing the existence of a common problem, tries to come to a collective decision. A high level of consensus among experts is needed before reaching a solution. It is customary to construct consensus measures by using similarity functions to quantify the closeness of experts preferences. The use of a metric that describes the distance between experts preferences allows the definition of similarity functions. Different distance functions have been proposed in order to implement consensus measures. This paper examines how the use of different aggregation operators affects the level of consensus achieved by experts through different distance functions, once the number of experts has been established in the GDM problem. In this situation, the experimental study performed establishes that the speed of the consensus process is significantly affected by the use of diverse aggregation operators and distance functions. Several decision support rules that can be useful in controlling the convergence speed of the consensus process are also derived.

In social network group decision making (SNGDM), the consensus reaching process (CRP) is used to help decision makers with social relationships reach consensus. Many CRP studies have been conducted in SNGDM until now. This paper provides a review of CRPs in SNGDM, and as a result it classifies them into two paradigms: (i) the CRP paradigm based on trust relationships, and (ii) the CRP paradigm based on opinion evolution. Furthermore, identified research challenges are put forward to advance this area of research.

A promising research area in the field of group decision making (GDM) is the study of interpersonal influence and its impact on the evolution of experts' opinions. In conventional GDM models, a group of experts express their individual preferences on a finite set of alternatives, then preferences are aggregated and the best alternative, satisfying the majority of experts, is selected. Nevertheless, in real situations, experts form their opinions in a complex interpersonal environment where preferences are liable to change due to social influence. In order to take into account the effects of social influence during the GDM process, we propose a new influence-guided GDM model based on the following assumptions: experts influence each other and the more an expert trusts in another expert, the more his opinion is influenced by that expert. The effects of social influence are especially relevant to cases when, due to domain complexity, limited expertise or pressure to make a decision, an expert is unable to express preferences on some alternatives, i.e., in presence of incomplete information. The proposed model adopts fuzzy rankings to collect both experts' preferences on available alternatives and trust statements on other experts. Starting from collected information, possibly incomplete, the configuration and the strengths of interpersonal influences are evaluated and represented through a social influence network (SIN). The SIN, in its turn, is used to estimate missing preferences and evolve them by simulating the effects of experts' interpersonal influence before aggregating them for the selection of the best alternative. The proposed model has been experimented with synthetic data to demonstrate the influence driven evolution of opinions and its convergence properties.

In large-scale group decision making (GDM), noncooperative behavior in the consensus reaching process (CRP) is not unusual. For example, some individuals might form a small alliance with the aim to refuse attempts to modify their preferences or even to move them against consensus to foster the alliance's own interests. In this paper, we propose a novel framework based on a self-management mechanism for noncooperative behaviors in large-scale CRPs (LCRPs). In the proposed consensus reaching framework, experts are classified into different subgroups using a clustering method, and experts provide their evaluation information, i.e., the multicriteria mutual evaluation matrices (MCMEMs), regarding the subgroups based on subgroups' performance (e.g., professional skills, cooperation, and fairness). The subgroups' weights are dynamically generated from the MCMEMs, which are in turn employed to update the individual experts' weights. This self-management mechanism in the LCRP allows penalizing the weights of the experts with noncooperative behaviors. Detailed simulation experiments and comparison analysis are presented to verify the validity of the proposed framework for managing noncooperative behaviors in the LCRP.

Intuitionistic fuzzy preference relations (IFPRs) are used to deal with hesitation, while interval-valued fuzzy preference relations (IVFPRs) are for uncertainty in multicriteria decision making (MCDM). This paper aims to explore the isomorphic multiplicative transitivity for IFPRs and IVFPRs, which builds the substantial relationship between hesitation and uncertainty in MCDM. To do that, the definition of the multiplicative transitivity property of IFPRs is established by combining the multiplication of intuitionistic fuzzy sets and Tanino's multiplicative transitivity property of fuzzy preference relations. It is proved to be isomorphic to the multiplicative transitivity of IVFPRs derived via Zadeh's extension principle. The use of the multiplicative transitivity isomorphism is twofold: 1) to discover the substantial relationship between IFPRs and IVFPRs, which will bridge the gap between hesitation and uncertainty in MCDM problems; and 2) to strengthen the soundness of the multiplicative transitivity property of IFPRs and IVFPRs by supporting each other with two different reliable sources, respectively. Furthermore, based on the existing isomorphism, the concept of multiplicative consistency for IFPRs is defined through a strict mathematical process, and it is proved to satisfy the following several desirable properties: weak transitivity, max-max transitivity, and center-division transitivity. A multiplicative consistency-based multiobjective programming (MOP) model is investigated to derive the priority vector from an IFPR. This model has the advantage of not losing information, as the priority vector representation coincides with that of the input information, which was not the case with the existing methods, where crisp priority vectors were derived as a consequence of the modeling transitivity just for the intuitionistic membership function and not for the intuitionistic nonmembership function. Finally, a numerical example concerning green supply selection is given to validate the efficiency and practicality of the proposed multiplicative consistency MOP model.

In Group Decision Making (GDM) problems before to obtain a solution a high level of consensus among experts is required. Consensus measures are usually built using similarity functions measuring how close experts' opinions or preferences are. Similarity functions are defined based on the use of a metric describing the distance between experts' opinions or preferences. Different distance functions have been proposed to implement consensus measures. This paper analyzes the effect of the application of different aggregation operators combined with the use of different distance functions for measuring consensus in GDM problems. It is concluded that the application of different aggregation operators together with different distance functions has a significant effect on the speed of achieving consensus. These results are analysed and used to derive decision support rules, based on a convergent criterion, that can be used to control the convergence speed of the consensus process using the compared distance functions.

Intuitionistic fuzzy preference relation are gaining increasing relevance in the field of group decision making as they provide the experts with means to allocate the uncertainty inherent in their proposed opinions. A key issue in this field is to reach a solution accepted by the majority of the members of the group. In this contribution we present a new confidence-consistency based consensus model. Moreover to rank the alternatives we present the implementation of Orlovsky's non-dominance concept to define the fuzzy quantifier guided non-dominance choice degree for intuitionistic fuzzy preference relations.

In the field of Sentiment Analysis, a number of different classifiers are utilised to attempt to establish the polarity of a given sentence. As such, there could be a need for aggregating the outputs of the algorithms involved in the classification effort. If the output of every classification algorithm resembles the opinion of an expert in the subject at hand, we are then in the presence of a group decision-making problem, which in turn translates into two sub-problems: (a) defining the desired semantic of the aggregation of all opinions, and (b) applying the proper aggregation technique that can achieve the desired semantic chosen in (a). The objective of this article is twofold. Firstly, we present two specific aggregation semantics, namely fuzzy-majority and compensatory, which are based on Induced Ordered Weighted Averaging and Uninorm operators, respectively. Secondly, we show the power of these two techniques by applying them to an existing hybrid method for classification of sentiments at the sentence level. In this case, the proposed aggregation solutions act as a complement in order to improve the performance of the aforementioned hybrid method. In more general terms, the proposed solutions could be used in the creation of semantic-sensitive ensemble methods, instead of the more simple ensemble choices available today in commercial machine learning software offerings.

In some real-world multiple attribute decision making (MADM) problems, a decision maker can strategically set attribute weights to obtain her/his desired ranking of alternatives, which is called the strategic weight manipulation of the MADM. Sometimes, the attribute weights are given with imprecise or partial information, which is called incomplete information of attribute weights. In this study, we propose the strategic weight manipulation under incomplete information on attributes weights. Then, a series of mixed 0-1 linear programming models (MLPMs) are proposed to derive a strategic weight vector for a desired ranking of an alternative. Finally, a numerical example is used to demonstrate the validity of our models.

A theoretical interaction consensus model in group decision making with distributed linguistic trust information is proposed. To do that, the concept of distributed linguists trust function (DLTF) is defined, and then the associated operational laws and aggregation operations are explored. Combing the expectation degree and uncertainty degrees, a ranking method for distributed linguists trust function is proposed. To identify the inconsistent experts, three levels of consensus degree with DLTF are calculated. After that, a novel feedback mechanism is activated to generate recommendation advices for the inconsistent experts to higher consensus degree. Therefore, the inconsistent experts are able to reach the threshold value of group consensus. Finally, after consensus has been achieved, a ranking order relation for distributed linguists trust functions is constructed to select the most appropriate alternative.

With the incorporation of web 2.0 frameworks the complexity of decision making situations has exponentially increased, involving in many cases many experts, and a potentially huge number of different alternatives, leading the experts to present uncertainty with the preferences provided. In this context, is where Intuitionist fuzzy preference relations plays a key roll as they provide the experts with means to allocate the uncertainty inherent in their proposed opinions. However, in many occasions the experts are unable to give a preference due to different reasons, therefore effective mechanism to cope with missing informations are more than necessary. In this contribution, we present a new GDM approach able to estimate the missing information and at the same time provide a mechanism to bring closer the experts opinions in a iterative process in which the experts confidence plays a key role.

In group decision making, there are many situations where the opinion of the majority of participants is critical. The scenarios could be multiple, like a number of doctors finding commonality on the diagnose of an illness or parliament members looking for consensus on an specific law being passed. In this article, we present a method that utilizes induced ordered weighted averaging (IOWA) operators to aggregate a majority opinion from a number of sentiment analysis (SA) classification systems, where the latter occupy the role usually taken by human decision-makers as typically seen in group decision situations. In this case, the numerical outputs of different SA classification methods are used as input to a specific IOWA operator that is semantically close to the fuzzy linguistic quantifier ‘most of’. The object of the aggregation will be the intensity of the previously determined sentence polarity in such a way that the results represent what the majority think. During the experimental phase, the use of the IOWA operator coupled with the linguistic quantifier ‘most’ () proved to yield superior results compared to those achieved when utilizing other techniques commonly applied when some sort of averaging is needed, such as arithmetic mean or median techniques.

This research presents a specialised extension to the genetic algorithms (GA) known as the genetic programming (GP) and gene expression programming (GEP) to explore and investigate the outcome of the GEP criteria on the stock market price prediction. The aim of this research is to model and predict short-to-medium term stock value fluctuations in the market via genetically tuned stock market parameters. The technology proposes a fractional adaptive mutation rate Elitism (GEP-FAMR) technique to initiate a balance between varied mutation rates and between varied-fitness chromosomes, thereby improving prediction accuracy and fitness improvement rate. The methodology is evaluated against different dataset and selection methods and showed promising results with a low error-rate in the resultant pattern matching with an overall accuracy of 95.96% for short-term 5-day and 95.35% for medium-term 56-day trading periods.

This contribution presents a hybrid approach to Sentiment Analysis (SA) encompassing the use of semantic rules, fuzzy sets, unsupervised machine learning techniques and a sentiment lexicon improved with the support of Senti-WordNet. A Hybrid Standard Classification is first carried out, which is further enhanced into a Hybrid Advanced approach incorporating linguistic classification of semantic polarity modelled using fuzzy sets. The mechanism of the new SA methodology is illustrated by applying it to compute the polarity of a given sentence and to a benchmarking publicly available dataset: the Movie Review Dataset.

Preference modelling based on Atanassov's intuitionistic fuzzy sets are gaining increasing relevance in the field of group decision making as they provide experts with a flexible and simple tool to express their preferences on a set of alternative options, while allowing, at the same time, to accommodate experts' preference uncertainty, which is inherent to all decision making processes. A key issue within this framework is the provision of efficient methods to rank alternatives, from best to worse, taking into account the peculiarities that this type of preference representation format presents. In this contribution we analyse the relationships between the main method proposed and used by researchers to rank alternatives using intuitionistic fuzzy sets, the score degree function, and the well known choice degree based on Orlovsky's non-dominance concept for the case when the preferences are expressed by means of fuzzy preference relations. This relationship study will provide the necessary theoretical results to support the implementation of Orlovsky's non-dominance concept to define the fuzzy quantifier guided non-dominance choice degree for intuitionistic fuzzy preference relations.

Data is frequently characterised by both uncertainty and seasonality. Type-2 fuzzy sets are an extension of type-1 fuzzy sets offering a conceptual scheme within which the effects of uncertainties in fuzzy inferencing may be modelled and minimised. Complex fuzzy sets are type-1 fuzzy sets extended by an additional phase term which permits them to intuitively represent the seasonal aspect of fuzziness in time-series applications. Type-2 fuzzy sets take two forms, generalised, and the simpler interval. Interval-valued fuzzy sets are type-1 fuzzy sets whose behaviour and properties are equivalent to interval type-2 fuzzy sets. This paper is concerned with the combination of interval-valued fuzzy sets and complex fuzzy sets to develop interval-valued complex fuzzy sets, an adaption of complex fuzzy sets such that the membership function assigns each point on the domain to an interval. From the definition of the interval-valued complex fuzzy set, the principles of interval-valued complex fuzzy logic are developed.

Preference relations are very useful to express decision makers' preferences over alternatives in the process of decision-making. However, multiple self-confidence levels are not considered in existing preference relations. In this study, we propose a new type of preference relations: fuzzy preference relations with self-confidence. A linear programming model is proposed for estimating priority vectors of this new type of preference relations. Finally, two numerical examples are provided to demonstrate the linear programming model, and a comparative analysis is used to show the influence of self-confidence levels on the decision-making results.

Citation classics offer an outlook on those papers that have attracted great and historical interest by a research community and that could be also considered the basis of the research field. A new approach, which is called H-Classics, has been developed to identify such highly cited papers. It is based on the H-index and is sensitive to both the own characteristics of the corresponding research discipline and its evolution. The present study provides a useful insight into the development of the intelligent transport systems research field, revealing those scientific actors (authors, countries, and institutions) that have made the biggest research contribution to its development.

Rule based classification or rule induction (RI) in data mining is an approach that normally generates classifiers containing simple yet effective rules. Most RI algorithms suffer from few drawbacks mainly related to rule pruning and rules sharing training data instances. In response to the above two issues, a new dynamic rule induction (DRI) method is proposed that utilises two thresholds to minimise the items search space. Whenever a rule is generated, DRI algorithm ensures that all candidate items' frequencies are updated to reflect the deletion of the rule's training data instances. Therefore, the remaining candidate items waiting to be added to other rules have dynamic frequencies rather static. This enables DRI to generate not only rules with 100% accuracy but rules with high accuracy as well. Experimental tests using a number of UCI data sets have been conducted using a number of RI algorithms. The results clearly show competitive performance in regards to classification accuracy and classifier size of DRI when compared to other RI algorithms.

Information aggregation is a key task in any group decision making problem. In the fuzzy linguistic context, when comparing two alternatives, it is usually assumed that assessments belong to linguistic term sets of symmetrically distributed labels with respect to a central label that stands for the indifference state. However, in practice there are many situations whose nature recommends their modelling using not symmetric linguistic term sets, and therefore formal approaches to deal with sets of unbalanced linguistic labels in decision making are necessary to be appropriately developed. In literature, the linguistic hierarchy methodology has proved successful when modelling unbalanced linguistic labels using an ordinal approach in their representation. However, linguistic labels can be modelled using a cardinal approach, i.e. as fuzzy subsets represented by membership functions. Obviously, the linguistic hierarchy methodology is not appropriate in these cases. In this contribution, a Type-1 OWA approach is proposed to deal with the aggregation step of the resolution process of a group decision making problem with unbalanced linguistic information modelled using a cardinal approach. The Type-1 OWA operator aggregates fuzzy sets and uses whole membership functions to compute the aggregated output fuzzy sets. The application of the Type-1 OWA approach to an example where the linguistic hierarchy approach was applied before will provide us an opportunity to compare the aggregated results obtained in both cases. Following the defuzzification of the Type-1 OWA aggregated values, it can be concluded that both methodologies are equivalent. The use of the Type-1 OWA approach in this decision making context does not require building linguistic hierarchies while at the same time allows a fully exploitation of the fuzzy nature of linguistic information.

Uncertainty, hesitation and vagueness are inherent to human beings when articulating opinions and preferences. Therefore in decision making situations it might well be the case that experts are unable to express their opinions in an accurate way. Under these circumstances, various families of preference relations (PRs) have been proposed (linguistic, intuitionistic and interval fuzzy PRs) to allow the experts to manifest some degree of hesitation when enunciating their opinions. An extreme case of uncertainty happens when an expert is unable to differentiate the degree up to which one preference is preferred to another. Henceforth, incomplete preference relations are possible. It is worth to bear in mind that incomplete information does not mean low quality information, on the contrary, in many occasions experts might prefer no to provide information in other to keep consistency. Consequently mechanism to deal with incomplete information in decision making are necessary. This contribution presents the main consistency based completion approaches to estimate incomplete preference values in linguistic, intuitionistic and interval fuzzy PRs.

Stock market prediction is of immense interest to trading companies and buyers due to high profit margins. Therefore, precise prediction of the measure of increase or decrease of stock prices also plays an important role in buying/selling activities. This research presents a specialised extension to the genetic algorithms (GA) known as the genetic programming (GP) and gene expression programming (GEP) to explore and investigate the outcome of the GEP criteria on the stock market price prediction. The research presented in this paper aims at the modelling and prediction of short-to-medium term stock value fluctuations in the market via genetically tuned stock market parameters. The technique uses hierarchically defined GP and GEP techniques to tune algebraic functions representing the fittest equation for stock market activities. The proposed methodology is evaluated against five well-known stock market companies with each having its own trading circumstances during the past 20+ years. The proposed GEP/GP methodologies were evaluated based on variable window/population sizes, selection methods, and Elitism, Rank and Roulette selection methods. The Elitism-based approach showed promising results with a low error-rate in the resultant pattern matching with an overall accuracy of 93.46% for short-term 5-day and 92.105 for medium-term 56-day trading periods.

With the appearance of Web 2.0 technologies, the way Internet is conceived has dramatically changed. Internet users have begun to perform a more active role in providing and sharing the information available on the Web. Thanks to mobile technologies, users can access the Internet from their smartphones at any time, independently of their location. Moreover, users gather in communities where they can communicate and share information. These communities can hold a high number of people and, consequently, a large amount of information need to be managed. Nevertheless, as the information tends to be disorganized, it is difficult for users to manage them properly to make the most of it. Therefore, there is a necessity of tools that can help users to organize and manage in a proper way the large amount of available information. In this paper, we propose the use of a novel group decision making approach to allow a high number of people to communicate among themselves and reach conclusions in a regulated way. As a high amount of people usually implies too much information, we propose the use of Fuzzy Ontologies as a way to deal with it in an organized way.

The decision-making assumption of all experts being able to express their preferences on all available alternatives of a decision-making problem might be considered unrealistic. This is specially true when the number of alternatives is considerable high and/or when sources of information are conflicting and dynamic. Thus, the presence of incomplete information, which is not equivalent to low quality information, is worth investigation and its processing within decision-making processes desirable. A consistency based approach to deal with incomplete fuzzy linguistic preferences is the focus of this contribution. Consistency is considered here as linked to the transitivity of preferences, and in particular to Tanino's multiplicative transitivity property of reciprocal fuzzy preference relations. The first result presented is the formal modelling and representation of Tanino's multiplicative transitivity property to the case of fuzzy linguistic preference relations. This is done via Zadeh's extension principle and the representation theorem of fuzzy sets. The second result derives the multiplicative transitivity property of reciprocal intuitionistic fuzzy preference relations, which can be isomorphically mapped to a particular type of linguistic preference relation: reciprocal interval-valued fuzzy preference relations. The third result is the computation of the consistency based estimated reciprocal intuitionistic fuzzy preference values using an indirect chain of alternatives, which can be used to address incomplete information in decision-making problems with this type of preference relations.

The multiplicative consistency (MC) property of interval additive reciprocal preference relations (IARPRs) is explored, and then the consistency index is quantified by the multiplicative consistency estimated IARPR. The MC property is used to measure the level of consistency of the information provided by the experts and also to propose the consistency index induced ordered weighted averaging (CI-IOWA) operator. The novelty of this operator is that it aggregates individual IARPRs in such a way that more importance is put on the most consistent ones. Finally, an approach for group decision making problems with IARPRs is proposed.

An important issue to bear in mind in Group Decision Making situations is that of consistency. However, the expression of consistent preferences is often a very difficult task for the decision makers, specially in decision problems with a high number of alternatives and when decision makers use fuzzy preference relations to provide their opinions. It leads to situations where a decision maker may not be able to express all his/her preferences properly and without contradiction. To overcome this problem, we propose the concept of the information granularity being regarded as an important and useful asset supporting the goal to reach consistent fuzzy preference relations. To do so, we develop a concept of granular fuzzy preference relation where each pairwise comparison is formed as a certain information granule instead of a single numeric value. As being more abstract, the granular format of the preference model offers the required flexibility to increase the level of consistency.

Classic aggregation operators in group decision making such as the ordered weighted averaging (OWA), induced ordered weighted averaging (IOWA), C-IOWA, P-IOWA, and I-IOWA have shown to be successful tools to provide flexibility in the aggregation of preferences. However, these operators do not take advantage of information related to the interaction between experts. Experts involved in a group decision-making problem may have developed opinions about the reliability of other experts' judgments, either because they have previous history of interaction with each other or because they have knowledge that informs them on the reliability of other colleagues in the group in solving decision-making problems in the past. In this paper, and within the framework of social network decision making, we present three new social network analysis based IOWA operators that take advantage of the linguistic trustworthiness information gathered from the experts' social network to aggregate the social group preferences. Their use is analysed with simple but illustrative examples.

In this paper, we highlight the conceptual structure of the intelligent transportation systems (ITS) research field in the period 1992-2011. To do that, an automatic approach for detecting and visualizing hidden themes and their evolution across a consecutive span of years is applied. This automatic approach, which is based on co-word analysis, combines performance analysis and science mapping. To show the conceptual evolution of ITS, three consecutive periods have been defined, i.e., 1992-2001, 2002-2006, and 2007-2011. We have identified that the ITS research has been focused on six main thematic areas, i.e., VEHICLE-AND-ROAD-TRACKING, DRIVER-BEHAVIOR-AND-SAFETY, SCENARIOS-SIMULATION, TRAFFIC-FLOW-AND-TRAFFIC-MANAGEMENT, VEHICLE-CONTROL, and VEHICLE-NAVIGATION.

For general type-2 fuzzy sets, the defuzzification process is very complex and the exhaustive direct method of implementing type-reduction is computationally expensive and turns out to be impractical. This has inevitably hindered the development of type-2 fuzzy inferencing systems in real-world applications. The present situation will not be expected to change, unless an efficient and fast method of deffuzzifying general type-2 fuzzy sets emerges. Type-1 ordered weighted averaging (OWA) operators have been proposed to aggregate expert uncertain knowledge expressed by type-1 fuzzy sets in decision making. In particular, the recently developed alpha-level approach to type-1 OWA operations has proven to be an effective tool for aggregating uncertain information with uncertain weights in real-time applications because its complexity is of linear order. In this paper, we prove that the mathematical representation of the type-reduced set (TRS) of a general type-2 fuzzy set is equivalent to that of a special case of type-1 OWA operator. This relationship opens up a new way of performing type reduction of general type-2 fuzzy sets, allowing the use of the alpha-level approach to type-1 OWA operations to compute the TRS of a general type-2 fuzzy set. As a result, a fast and efficient method of computing the centroid of general type-2 fuzzy sets is realized. The experimental results presented here illustrate the effectiveness of this method in conducting type reduction of different general type-2 fuzzy sets.

Collaborative Filtering Recommender Systems are one of the most used and well-known tools in the e-commerce area because they are adaptive and they do not need information about the recommended items. Although many studies have been proposed to take advantage of the information gathered by this kind of recommender systems, none have focused on the use of social network analysis. In this contribution we present a first approach that shows some of the advantages and results that can be obtained applying this methodology.

Type-1 Ordered Weighted Averaging (OWA) operator provides us with a new technique for directly aggregating uncertain information with uncertain weights via OWA mechanism in soft decision making and data mining, in which uncertain objects are modeled by fuzzy sets. The Direct Approach to performing type-1 OWA operation involves high computational overhead. In this paper, we define a type-1 OWA operator based on the \alpha-cuts of fuzzy sets. Then, we prove a Representation Theorem of type-1 OWA operators, by which type-1 OWA operators can be decomposed into a series of \alpha-level type-1 OWA operators. Furthermore, we suggest a fast approach, called Alpha-Level Approach, to implementing the type-1 OWA operator. A practical application of type-1 OWA operators to breast cancer treatments is addressed. Experimental results and theoretical analyses show that: 1) the Alpha-Level Approach with linear order complexity can achieve much higher computing efficiency in performing type-1 OWA operation than the existing Direct Approach, 2) the type-1 OWA operators exhibit different aggregation behaviors from the existing fuzzy weighted averaging (FWA) operators, and 3) the type-1 OWA operators demonstrate the ability to efficiently aggregate uncertain information with uncertain weights in solving real-world soft decision-making problems.

In this paper two contrasting approaches to the defuzzification of generalised type-2 fuzzy sets are investigated. The sampling method is a direct approach, whereas the α-planes method extends interval defuzzification to generalised type-2 sets, and therefore has to be used in conjunction with an interval technique such as the Karnik-Mendel Iterative Procedure. Experimental evaluations are made of the sampling and α-planes methods, with respect to both efficiency and accuracy, showing both strategies to be efficient and good approximations.

Yager's ordered weighted averaging (OWA) operator has been widely used in soft decision making to aggregate experts' individual opinions or preferences for achieving an overall decision. The traditional Yager's OWA operator focuses exclusively on the aggregation of crisp numbers. However, human experts usually tend to express their opinions or preferences in a very natural way via linguistic terms. Type-2 fuzzy sets provide an efficient way of knowledge representation for modeling linguistic terms. In order to aggregate linguistic opinions via OWA mechanism, we propose a new type of OWA operator, termed type-2 OWA operator, to aggregate the linguistic opinions or preferences in human decision making modeled by type-2 fuzzy sets. A Direct Approach to aggregating interval type-2 fuzzy sets by type-2 OWA operator is suggested in this paper. Some examples are provided to delineate the proposed technique. © 2010 Wiley Periodicals, Inc.

We begin by surveying the available strategies for type-reducing a discretised type-2 fuzzy set to a type-1 fuzzy set, namely the exhaustive method, the Karnik-Mendel Iterative Procedure, the sampling method, the Greenfield-Chiclana Collapsing Defuzzifier and the Nie-Tan method. We go on to investigate mathematically what happens to the Representative Embedded Set Approximation as the domain discretisation becomes finer. This leads into a discussion of the relationship between the collapsing and Nie-Tan methods. An experimental comparison is made between the collapsing and Nie-Tan methods, with respect to both efficiency and accuracy.

In this paper, a novel type-1 OWA based non-stationary fuzzy system is proposed, in which the type-1 OWA operator is used in the fuzzy inference process to aggregate the non-stationary fuzzy outputs. The advantage of non-stationary fuzzy sets lies in their ability to model expert's variations in automated decision support systems. The proposed scheme offers an opportunity to combine different uncertain objects with uncertain weights into an overall decision in the fuzzy inference process. The agreement achieved between the proposed fuzzy system and clinical expert decision in selecting optimal treatment plans is used to evaluate the performance of the method. The experimental results on post-operative breast cancer treatments have demonstrated that the proposed fuzzy system can effectively diagnose breast cancer treatment in decision supports.

The aim of this paper is to propose a procedure to estimate missing preference values when dealing with incomplete fuzzy linguistic preference relations assessed using a two-tuple fuzzy linguistic approach. This procedure attempts to estimate the missing information in an individual incomplete fuzzy linguistic preference relation using only the preference values provided by the respective expert. It is guided by the additive consistency property to maintain experts' consistency levels. Additionally, we present a selection process of alternatives in group decision making with incomplete fuzzy linguistic preference relations and analyze the use of our estimation procedure in the decision process. © 2008 Wiley Periodicals, Inc.

Most existing distances between intuitionistic fuzzy sets are defined in linear plane representations in 2D or 3D space. Here, we define a new interpretation of intuitionistic fuzzy sets as a restricted spherical surface in 3D space. A new spherical distance for intuitionistic fuzzy sets is introduced. We prove that the spherical distance is different from those existing distances in that it is nonlinear with respect to the change of the corresponding fuzzy membership degrees. © 2009 Wiley Periodicals, Inc.

Consistency of preferences is related to rationality, which is associated with thetransitivityproperty. Many properties suggested to model transitivity of preferences are inappropriate for reciprocal preference relations. In this paper, a functional equation is put forward to model the ldquocardinal consistency in the strength of preferencesrdquo of reciprocal preference relations. We show that under the assumptions of continuity and monotonicity properties, the set of representable uninorm operators is characterized as the solution to this functional equation. Cardinal consistency with the conjunctive representable cross ratio uninorm is equivalent to Tanino's multiplicative transitivity property. Because any two representable uninorms are order isomorphic, we conclude that multiplicative transitivity is the most appropriate property for modeling cardinal consistency of reciprocal preference relations. Results toward the characterization of this uninorm consistency property based on a restricted set of (n-1) preference values, which can be used in practical cases to construct perfect consistent preference relations, are also presented.

Type-2 fuzzy systems are increasing in popularity, and there are many examples of successful applications. While many techniques have been proposed for creating parsimonious type-1 fuzzy systems, there is a lack of such techniques for type-2 systems. The essential problem is to reduce the number of rules, while maintaining the system's approximation performance. In this paper, four novel indexes for ranking the relative contribution of type-2 fuzzy rules are proposed, which are termedR-values,c-values, omega1-values, and omega2-values. TheR-values of type-2 fuzzy rules are obtained by applying a QR decomposition pivoting algorithm to the firing strength matrices of the trained fuzzy model. Thec-values rank rules based on the effects of rule consequents, while the omega1-values and omega2-values consider both the rule-base structure (via firing strength matrices) and the output contribution of fuzzy rule consequents. Two procedures for utilizing these indexes in fuzzy rule selection (termed ldquoforward selectionrdquo and ldquobackward eliminationrdquo) are described. Experiments are presented which demonstrate that by using the proposed methodology, the most influential type-2 fuzzy rules can be effectively retained in order to construct parsimonious type-2 fuzzy models.

This note analyzes two methods for calculating missing values of an incomplete reciprocal fuzzy preference relation. The first method by Herrera-Viedma appeared in the IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics [vol. 37, no. 1 (2007) 176-189], while the second one by Fedrizzi and Giove appeared later in the European Journal of Operational Research [vol. 183 (2007) 303-313]. The underlying concept driving both methods is the additive consistency property. We show that both methods, although different, are very similar. Both methods derive the same estimated values for the independent-missing-comparison case, while they differ in the dependent-missing-comparison case. However, it is shown that a modification of the first method coincides with the second one. Regarding the total reconstruction of an incomplete preference relation, it is true that the second method performs worse than the first one. When Herrera-Viedma 's method is unsuccessful, Fedrizzi-Giove's method is as well. However, in those cases when Fedrizzi-Giove's method cannot guarantee the successful reconstruction of an incomplete preference relation, we have that Herrera-Viedma 's method can. These results lead us to claim that both methods should be seen as complementary rather than competitors in their application, and as such, we propose a reconstruction policy of incomplete fuzzy preference relations using both methods. By doing this, the only unsuccessful reconstruction case is when there is a chain of missing pairwise comparisons involving each one of the feasible alternatives at least once.

Under a set of conditions consistency of fuzzy preference relations can be characterised by almost continuous self-dual uninorms. Consequently, the concept of U-consistent fuzzy preference relation is introduced. Amongst the many consistency properties proposed for reciprocal fuzzy preference relations, Taninopsilas multiplicative transitivity property, being an example of such type of uninorms, seems to be an appropriate U-consistency property for reciprocal fuzzy preference relations. We present results towards the characterization of the U-consistency property of a fuzzy preference relation based on a restricted set of n-1 preference values, which can be used in practical cases to construct perfect U-consistent preference relations.

Type-1 OWA operators provide an efficient way of aggregating linguistic opinions in the form of type-1 fuzzy sets for decision-makers. Like in Yager’s OWA operations, the identification of an appropriate type-1 OWA operator, i.e., to determine the linguistic weights in the form of type-1 fuzzy sets, is crucial in type-1 OWA based aggregation. Indeed, these weights reflect the decision-makers’ desired agenda for aggregating the preferences or criteria. In this paper, for the sake of identifying linguistic weights used in the type-1 OWA operators, type-2 linguistic quantifiers are proposed, in which the higher level of uncertainty of linguistic quantifiers is modelled by type-2 fuzzy sets. Some examples are provided to illustrate the proposed concepts.

Yager’s ordered weighted averaging (OWA) operator has been widely used in soft decision making to aggregate experts’ individual opinions or preferences for achieving an overall decision. The traditional Yager’s OWA operator focuses exclusively on the aggregation of crisp numbers. However, human experts usually tend to express their opinions or preferences in a very natural way via linguistic terms, like “important” , “very important”, “good” etc.. Type-2 fuzzy sets provide an efficient way of knowledge representation for modelling linguistic terms. In order to aggregate linguistic opinions via the OWA mechanism, we propose a new type of OWA operator, termed type-2 OWA operator that is able to aggregate type-2 fuzzy sets, and therefore to aggregate the linguistic opinions or preferences in human decision making. The necessary equations for performing type-2 OWA operations on aggregating interval type-2 fuzzy sets are derived in this paper. Some examples are provided to illustrate the proposed technique.

In this paper, we present a procedure to estimate missing preference values when dealing with pairwise comparison and heterogeneous information. This procedure attempts to estimate the missing information in an expert's incomplete preference relation using only the preference values provided by that particular expert. Our procedure to estimate missing values can be applied to incomplete fuzzy, multiplicative, interval-valued, and linguistic preference relations. Clearly, it would be desirable to maintain experts' consistency levels. We make use of the additive consistency property to measure the level of consistency and to guide the procedure in the estimation of the missing values. Finally, conditions that guarantee the success of our procedure in the estimation of all the missing values of an incomplete preference relation are given. © 2008 Wiley Periodicals, Inc.

Dealing with incomplete information is an important problem in decision making. In this paper, we present a short discussion on this topic and a new estimation method of missing values in an incomplete fuzzy preference relation which is based on the modelling of consistency of preferences via a representable uninorm.

In group decision making (GDM) processes, prior to the selection of the best alternative(s), it would be desirable that experts achieve a high degree of consensus or agreement between them. Due to the complexity of most decision making problems, individuals' preferences may not satisfy formal properties. ‘Consistency’ is one of such properties, and it is associated with the transitivity property. Obviously, when carrying out a rational decision making, consistent information, i.e. information which does not imply any kind of contradiction, is more appropriate than information containing some contradictions. Therefore, in a GDM process, consistency should also be sought after. In this paper we present a consensus model for GDM problems that proceeds from consistency to consensus. This model integrates a novel consistency reaching module based on consistency measures. In particular, the model generates advice on how experts should change their preferences in order to increase their consistency. Also, the consensus model is considered adaptive because the search for consensus is adapted to the level of agreement achieved at each consensus round.

In the resolution of group decision making problems the consensus process, that is, the process where experts discuss about the alternatives to narrow their differences, is usually held with all the experts gathered together in a place where they can speak and discuss about the alternatives in the problem. However, in situations where it is not possible to bring them all together it is usually difficult for the experts to identify the closeness of the opinions of the rest of the experts, and thus, it can be difficult to have a clear view of the current state of the consensus process. In this paper we present a tool that creates consensus diagrams that help experts to easily comprehend the current consensus state in the decision problem. This tool is based on several consistency, consensus and similarity measures and with the application of a clustering algorithm, it identifies and represents the different groups of experts with similar opinions, identifies a possible candidate for spokesperson for each group and easily depicts the consistency level expressed by each one of the experts.

The consistency of reciprocal preference relations is studied. Consistency is related with rationality, which is associated with the transitivity property. For fuzzy preference relations many properties have been suggested to model transitivity and, consequently, consistency may be measured according to which of these different properties is required to be satisfied. However, we will show that many of them are not appropriate for reciprocal preference relations. We put forward a functional equation to model consistency of reciprocal preference relations, and show that self-dual uninorms operators are the solutions to it. In particular, Tanino's multiplicative transitivity property being an example of such type of uninorms seems to be an appropriate consistency property for fuzzy reciprocal preferences.

In this paper, we propose two novel indices for type-2 fuzzy rule ranking to identify the most influential fuzzy rules in designing type-2 fuzzy logic systems, and name them as R-values and c-values of fuzzy rules separately. The R-values of type-2 fuzzy rules are obtained by applying QR decomposition in which there is no need to estimate a rank as required in the SVD-QR with column pivoting algorithm. The c-values of type-2 fuzzy rules are suggested to rank rules based on the effects of rule consequents. Experimental results on a signal recovery problem have shown that by using the proposed indices the most influential type-2 fuzzy rules can be effectively selected to construct parsimonious type-2 fuzzy models while the system performances are kept at a satisfied level.

Two processes are necessary to solve group decision making problems: A consensus process and a selection process. The consensus reaching process is necessary to obtain a final solution with a certain level of agreement between the experts; and the selection process is necessary to obtain such a final solution. In a previous paper, we present a selection process to deal with group decision making problems with incomplete fuzzy preference relations, which uses consistency measures to estimate the incomplete fuzzy preference relations. In this paper we present a consensus model. The main novelty of this consensus model is that of being guided by both consensus and consistency measures. Also, the consensus reaching process is guided automatically, without moderator, through both consensus and consistency criteria. To do that, a feedback mechanism is developed to generate advice on how experts should change or complete their preferences in order to reach a solution with high consensus and consistency degrees. In each consensus round, experts are given information on how to change their preferences, and to estimate missing values if their corresponding preference relation is incomplete. Additionally, a consensus and consistency based induced ordered weighted averaging operator to aggregate the experts' preferences is introduced, which can be used in consensus models as well as in selection processes. The main improvement of this consensus model is that it supports the management of incomplete information and it allows to achieve consistent solutions with a great level of agreement.

In decision-making problems there may be cases in which experts do not have an in-depth knowledge of the problem to be solved. In such cases, experts may not put their opinion forward about certain aspects of the problem, and as a result they may present incomplete preferences, i.e., some preference values may not be given or may be missing. In this paper, we present a new model for group decision making in which experts' preferences can be expressed as incomplete fuzzy preference relations. As part of this decision model, we propose an iterative procedure to estimate the missing information in an expert's incomplete fuzzy preference relation. This procedure is guided by the additive-consistency (AC) property and only uses the preference values the expert provides. The AC property is also used to measure the level of consistency of the information provided by the experts and also to propose a new induced ordered weighted averaging (IOWA) operator, the AC-IOWA operator, which permits the aggregation of the experts' preferences in such a way that more importance is given to the most consistent ones. Finally, the selection of the solution set of alternatives according to the fuzzy majority of the experts is based on two quantifier-guided choice degrees: the dominance and the nondominance degree.

The group decision-making framework with linguistic preference relations is studied. In this context, we assume that there exist several experts who may have different background and knowledge to solve a particular problem and, therefore, different linguistic term sets (multigranular linguistic information) could be used to express their opinions. The aim of this paper is to present a model of consensus support system to assist the experts in all phases of the consensus reaching process of group decision-making problems with multigranular linguistic preference relations. This consensus support system model is based on i) a multigranular linguistic methodology, ii) two consensus criteria, consensus degrees and proximity measures, and iii) a guidance advice system. The multigranular linguistic methodology permits the unification of the different linguistic domains to facilitate the calculus of consensus degrees and proximity measures on the basis of experts' opinions. The consensus degrees assess the agreement amongst all the experts' opinions, while the proximity measures are used to find out how far the individual opinions are from the group opinion. The guidance advice system integrated in the consensus support system model acts as a feedback mechanism, and it is based on a set of advice rules to help the experts change their opinions and to find out which direction that change should follow in order to obtain the highest degree of consensus possible. There are two main advantages provided by this model of consensus support system. Firstly, its ability to cope with group decision-making problems with multigranular linguistic preference relations, and, secondly, the figure of the moderator, traditionally presents in the consensus reaching process, is replaced by the guidance advice system, and in such a way, the whole group decision-making process is automated

In this article, we introduce the induced ordered weighted geometric (IOWG) operator and its properties. This is a more general type of OWG operator, which is based on the induced ordered weighted averaging (IOWA) operator. We provide some IOWG operators to aggregate multiplicative preference relations in group decision-making (GDM) problems. In particular, we present the importance IOWG (I-IOWG) operator, which induces the ordering of the argument values based on the importance of the information sources; the consistency IOWG (C-IOWG) operator, which induces the ordering of the argument values based on the consistency of the information sources; and the preference IOWG (P-IOWG) operator, which induces the ordering of the argument values based on the relative preference values associated with each one of them. We also provide a procedure to deal with “ties” regarding the ordering induced by the application of one of these IOWG operators. This procedure consists of a sequential application of the aforementioned IOWG operators. Finally, we analyze the reciprocity and consistency properties of the collective multiplicative preference relations obtained using IOWG operators. © 2004 Wiley Periodicals, Inc.

The ordered weighted geometric (OWG) operator is an aggregation operator that is based on the ordered weighted averaging (OWA) operator and the geometric mean. Its application in multicriteria decision making (MCDM) under multiplicative preference relations has been presented. Some families of OWG operators have been defined. In this article, we present the origin of the OWG operator and we review its relationship to the OWA operator in MCDM models. We show a study of its use in multiplicative decision-making models by providing the conditions under which reciprocity and consistency properties are maintained in the aggregation of multiplicative preference relations performed in the selection process. © 2003 Wiley Periodicals, Inc.

In this paper, we present a consensus model for multiperson decision making (MPDM) problems with different preference structures based on two consensus criteria: 1) a consensus measure which indicates the agreement between experts' opinions and 2) a measure of proximity to find out how far the individual opinions are from the group opinion. These measures are calculated by comparing the positions of the alternatives between the individual solutions and collective solution. In such a way, the consensus situation is evaluated in each moment in a more realistic way. With these measures, we design a consensus support system that is able to substitute the actions of the moderator. In this system, the consensus measure is used to guide the consensus process until the final solution is achieved while the proximity measure is used to guide the discussion phases of the consensus process. The consensus support system has a feedback mechanism to guide the discussion phases based on the proximity measure. This feedback mechanism is based on simple and easy rules to help experts change their opinions in order to obtain a degree of consensus as high as possible. The main improvement of this consensus model is that it supports consensus process automatically, without moderator, and, in such a way, the possible subjectivity that the moderator can introduce in the consensus process is avoided.