Due to the growing needs in decision-making under uncertainty, existing studies introduced consistency and consensus-driven algorithms for group decision-making (GDM) problems with hesitant fuzzy linguistic preference relations (HFLPRs). A decision support system (DSS) that can host these GDM algorithms to provide decision-support services or tools for practical use is urgently needed. However, the state-of-the-art architectures cannot organize these algorithms and related data to run within one framework. This is mainly due to the running environments for these GDM algorithms are different since these algorithms were not originally designed to be compatible. Given the multilingual consistency and consensus-based decision support algorithms, how to design and implement a cloud-based DSS in a multilingual environment is still an open question. To fill this gap, this paper provides a web-based and cloud-based DSS with a novel architecture that utilizes the advantages of microservices. The proposed system implements a multilingual support framework to dynamically upload, manage and run multilingual consistency and consensus-based decision support algorithms. An algorithm recommendation module is developed to help users choose suitable decision support algorithms. Tokenization is applied to deal with regulatory issues of knowledge protection, data privacy, and security while storing, analyzing, and transforming data into different algorithms for effective decision-making. An expert feedback study verified that our web and cloud-based DSS is a right artifact to fulfill the objective claimed in this paper.

Many group decision making (GDM) models enable experts to use only one preference information representation form. It is natural to allow experts to express preferences in various formats considering the heterogeneity of experts. In this case, how to reach the consensus of a group from heterogeneous preference information is an attractive research issue. This study proposes a consensus reaching process for large-scale GDM with heterogeneous preference information. First, we review various preference formats including preference orderings, numerical assessments, interval-valued assessments, and linguistic assessments. To facilitate the heterogeneous information aggregation, we classify experts into subgroups according to their preference types rather than the similarities of preference values, and then aggregate the homogeneous preference values in each subgroup. The subgroup priorities derived by homogeneous methods are then aggregated into global priorities. An ordinal consensus measuring process based on individual orderings is introduced. To reach the ordinal consensus, optimization models are constructed to ensure each subgroup's preferences equivalent to the global preferences, and the recommended ranges and strength of preference modification are given to experts. Finally, the proposed method is validated by an illustrative example about blockchain platform selection.

The evaluation and selection of cold chain logistics distribution centers are of vital importance for third-party logistics companies which want to build green cold chain logistics networks. To select distribution centers, the conflicts among multiple criteria should be considered. The combined compromise solutions (CoCoSo) method can help enterprises make a structural decision; however, in the original CoCoSo method, the evaluation information was expressed by crisp numbers. Nevertheless, in many cases, because of the imprecision and incompleteness of information, it may be more flexible for evaluators to provide imprecise and fuzzy values rather than crisp numbers. In addition, the judgment values are often expressed based on decision-makers' psychological expectations. The evaluation criteria of alternatives have relevance to some extent, which would influence the evaluation results. Based on these concerns, this study presents a modified CoCoSo method in the Pythagorean fuzzy environment in which evaluators can express psychological expectations on alternatives. To achieve this goal, the cumulative prospect theory is introduced to obtain the Pythagorean fuzzy prospect weights. Then, an objective weight determination method of criteria under the Pythagorean fuzzy environment is proposed to eliminate the influence of homogeneity of criteria. Based on the Pythagorean fuzzy prospect weights and the combined weights, the original CoCoSo method is extended to the Pythagorean fuzzy environment. A case of selection logistics distribution center is investigated to demonstrate the practicality of the proposed method. The advantages of the proposed method are verified by comparative analysis.

The probabilistic linguistic term set is a flexible and efficient tool to represent the cognitive complex information of experts. It has attracted many scholars’ attention since it was proposed. Information fusion over the cognitive complex information is a significant issue for decision-making problems. Over the past years, more than 40 aggregation operators have been proposed to fuse the probabilistic linguistic term sets. The aim of this paper is to survey the existing probabilistic linguistic aggregation operators from the perspectives of principles, definitions, classifications, and applications. To do so, first, we summarize the present normalization techniques and operations of probabilistic linguistic term sets. Afterward, this study classifies the existing probabilistic linguistic aggregation operators into 12 kinds. Then, the application areas of these probabilistic linguistic aggregation operators are outlined. Future research directions with interests are proposed to tackle present challenges.

The q-rung orthopair fuzzy set is characterized by membership and nonmembership functions, and the sum of the qth power of them is less than or equal to one. Since it releases the constraints existed in both intuitionistic fuzzy set and Pythagorean fuzzy set, it has wide applications in real cases. However, so far, there is little research on the multiplicative consistency of q-rung orthopair fuzzy preference relation (q-ROFPR). To fill this vacancy, this paper provides a detailed analysis on the multiplicative consistency of q-ROFPR. First, we investigate the concept of multiplicative consistent q-ROFPR and its properties. Subsequently, two goal programming models are proposed to derive the priorities from individual and group q-ROFPRs, respectively. After that, a novel consistency-improving algorithm for q-ROFPR and a weight-generating method for decision-makers are discussed in detail, based on which, a novel group decision-making method is proposed. Finally, a case study concerning the evaluation of rehabilitation program selection is given to illustrate the applicability of the proposed method. The effectiveness and superiority of the proposed method are verified by comparing it with some existing methods.

The q-rung orthopair fuzzy set, whose membership function and nonmembership function belong to the interval [0,1], is more powerful than both intuitionistic fuzzy set and Pythagorean fuzzy set in expressing imprecise information of decision-makers. The aim of this paper is to investigate a method to determine the priority weights from individual or group q-rung orthopair fuzzy preference relations (q-ROFPRs). To do so, firstly, a new definition of additively consistent q-ROFPR is presented based on the preference relation of alternatives given by decision-makers. Afterward, according to individual and group q-ROFPRs, two kinds of goal programming models are proposed, respectively, to generate the q-rung orthopair fuzzy priority weight vector of the given q-ROFPR(s). Finally, two numerical examples are given to illustrate the effectiveness and superiority of the method proposed in this paper.

Hesitant fuzzy linguistic term set (HFLTS) is a very useful technology in dealing with decision-making problems where people have hesitancy in providing their linguistic assessments. Distinct methods have been developed to aid decision making with HFLTSs, yet there is little research involving the issue that how to deal with the multigranularity hesitant fuzzy linguistic information. The aim of this paper is to develop the aggregation method for multigranularity hesitant fuzzy linguistic information and solve the linguistic group decision problem with different linguistic term sets. To do so, we first modify the translation functions and aggregation operators in the existing 2-tuple linguistic representation models so as to aggregate linguistic terms from different linguistic term sets. Then, we introduce the notion of hesitant 2-tuple sets to make computation of HFLTSs without loss of information, and develop some new operators to aggregate HFLTSs from different linguistic term sets. Using these operators, we propose a method to deal with multigranularity linguistic group decision-making problems with different situations where importance weights of either criteria or experts are known or unknown. Finally, the multigranularity linguistic group decision-making model is implemented to the healthcare waste treatment in West China Hospital to validate its effectiveness and efficiency in aiding decision-making process.

Intuitionistic fuzzy sets (IFSs) have attracted more and more scholars’ attention due to their powerfulness in expressing vagueness and uncertainty. In the course of decision making with IFSs, aggregation operators play a very important role since they can be used to synthesize multidimensional evaluation values represented as intuitionistic fuzzy values into collective values. This paper proposes a family of intuitionistic fuzzy hybrid weighted aggregation operators, such as the intuitionistic fuzzy hybrid weighted averaging operator, the intuitionistic fuzzy hybrid weighted geometric operator, the generalized intuitionistic fuzzy hybrid weighted averaging operator, and the generalized intuitionistic fuzzy hybrid weighted geometric operator. All these newly developed operators not only can weight both the arguments and their ordered positions simultaneously but also have some desirable properties, such as idempotency, boundedness, and monotonicity. To show the applications of our proposed intuitionistic fuzzy hybrid weighted aggregation operators, a simple schema for decision making with intuitionistic fuzzy information is developed. An example concerning the human resource management is given to illustrate the validity and applicability of the proposed method and also the hybrid weighted aggregation operators.