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.

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.

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.

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 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.

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.

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.

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.

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.

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.

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.

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.