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In group decision making (GDM), there are seldom ideal scenarios that all the preference information given by all individuals reach a highly level of agreement. Conflicts are present in the information fusion process and decision makers (DMs) have to negotiate and reconcile differences. To address this issue, it becomes inevitable to consider intelligent GDM method. In this article, we propose the granular neural network (GNN) to realize the aggregation process from the perspective of granular computing and machine learning. Our study is involved in an extension of best–worst method to the GDM scenario. The procedure is outlined as follows: first, information granules are allocated around the prototype of individuals’ preferences, complying with the principle of justifiable granularity. Thereby, the granular inputs are brought into a well-trained GNN. An adaptive particle swarm optimization algorithm is applied to optimize allocation of information granules. We calculate the threshold of consistency index for this granular model. Finally, a case study about hotel selection on Booking.com is presented to illustrate the performance of the proposed model. In addition, we use the stochastic analysis method to randomize the weights of group members with the objective to assess the robustness of the model. The feasibility and validity of the model are demonstrated by completing comparative analysis. The originality of this article is to establish a real data-driven granular GDM model both considering the optimization of group consistency and consensus.

• We develop a novel mechanism for MCGDM problems in BWM with an optimal allocation of information granularity. • We design the interval-based granules to formulate the entries of pairwise comparison vectors of BWM by using the principle of justifiable. • A novel distance function is proposed to measure the consensus degree among the group. • A case study of vehicle recommendation based on the online reviews on autohome.com is exhibited. In a multiple-criteria group decision-making process, it may be unrealistic to assume that all experts are specialized in all aspects of the entire problem and can reach full agreement. To obtain a suitable result with more flexibility and robustness in group decision-making, this study concerns the introduction of information granules to the best-worst method model, regarded as an essential design asset to reach a consensus in a group decision-making scenario. More specifically, each pairwise comparison is performed through information granules instead of single numbers, by using an optimal allocation of information granularity. Further, we develop an optimization model that considers both consistency and consensus in one problem. The particle swarm optimization algorithm is used as an optimization method to find the optimal particle of the granular decision model. Furthermore, a new convergent iterative algorithm is developed to obtain the desired decision matrix. Next, an experimental study is presented to demonstrate the effectiveness, flexibility, and essence of the proposed model. Finally, a case study of autohome.com is conducted to select suitable automobiles for a company based on online reviews. The solving procedures are demonstrated, to further illustrate the feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

• Propose an integrated method for product ranking through online reviews. • A complete framework to solve the ranking problem is developed. • A data-driven method of applying ER theory to sentiment analysis is proposed. • An MCDM-based method of ranking products with SD and PROMETHEE-II is proposed. • Propose an SMAA-PROMETHEE method for sensitivity analysis of the parameters. Online reviews play an important role in consumers' purchasing decisions. However, many online reviews confuse consumers when they wish to make a purchase but lack experience. To solve the problem of product ranking based on online reviews, two important issues must be addressed: sentiment analysis and product ranking based on multi-criteria decision-making (MCDM) methods. Therefore, this paper proposes an integrated MCDM method for product ranking through online reviews based on evidential reasoning (ER) theory and stochastic dominance (SD) rules. First, online reviews are preprocessed to obtain product attributes and weight values. Then, we use naive Bayes (NB), logistic regression (LR), and support vector machines (SVM) for the sentiment analysis of online reviews, and the results of the three classifiers are aggregated using ER theory. In addition, according to the confidence distribution matrix of sentiment orientations, SD rules are used to determine the stochastic dominance relations between pairwise alternatives for each attribute. Furthermore, we use the stochastic multi-criteria acceptability analysis (SMAA)-PROMETHEE method to obtain the final product ranking results and conduct sensitivity analysis. Finally, a case study on ranking computer products from JD Mall through online reviews is provided to illustrate the validity of the proposed method. [ABSTRACT FROM AUTHOR]

• Context-Dependent DEASort is proposed based on BWM for multi-criteria sorting problem. • Categories can be simply obtained without predefined classification categorical rules. • A common set of weight model is introduced for evaluating attractiveness of each DMU. • Case study concerning risk assessment of Yangtze River Economic Zone is provided. • Sensitivity analysis is conducted to illustrate the stability of the proposed method. With the increasing urban economic development and awareness of environment protection, ecological risk assessment (ERA), as a management mode combined with ecological research and risk assessment, has become a highly relevant topic in environment sustainable development. In this paper, we propose a novel sorting model based on Data Envelopment Analysis (DEA) and Best Worst method (BWM) to solve multi-criteria sorting problems and apply it to ERA. The proposed Context-Dependent DEASort method based on the idea of Context-Dependent DEA to position decision-making units (DMUs) into diverse categories in uncertain circumstance. It also takes experts' preference into full account as well, which makes the sorting solution more flexible and reasonable. Besides, a common set of weight-based model is introduced to deal with the situation when evaluating attractiveness and progress of each DMU. The common weight set model can ensure to provide an overall evaluation context compared to the original Context-Dependent DEA model, which only distinct the DMU from a single virtual DMU. Furthermore, a case study concerning ecological risk assessment of Yangtze River Economic Zone in China is provided to illustrate the applicability of the developed environment. Finally, comparative analysis and sensitivity analysis are carried out to demonstrate the practicality and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

• A heterogeneous QUALIFLEX method is proposed considering criteria interaction to solve MCGDM problem. • A new and visual graphical representation of criteria interaction is developed. • An identification method of the 2-order additive fuzzy measure is presented by means of group consensus. • A green supplier selection example is provided and a comparative analysis is performed. • An indirect method is given to deal with the fusion of interval number, trapezoidal fuzzy number, intuitionistic fuzzy number and hesitant fuzzy number. Green supplier selection complexity involves such problems which usually need to offer the management of dependencies among criteria in the selection process. Meanwhile, heterogeneous contexts are adopted based on different criteria, which drives to propose a novel multi-criteria group decision making (MCGDM) method. To solve this problem, this paper proposes a new MCGDM approach for heterogeneous information and dependent criteria based on the QUALItative FLEXible (QUALIFLEX) method and Choquet integral. For managing dependency among criteria, a new graphical representation of criteria interaction is presented and the identification of fuzzy measure is then obtained considering group consensus reaching. The multi-criteria heterogeneous QUALIFLEX method with regard to dependency of criteria is finally applied to a green supplier selection problem and a comparative analysis is performed to illustrate its feasibility and effectiveness. [ABSTRACT FROM AUTHOR]

Large-scale group decision-making (LSGDM) in a social network environment requires the collaborative consideration of large-scale decision-makers, social network structure, and consensus-reaching, which involves significant features of the social network, such as community structure, interpersonal relationships, and position value. In this study, we explore the driving role of social networks in the consensus-reaching process from the perspective of structural holes and construct a social network-driven bi-level minimum cost consensus model (MCCM) for LSGDM. The bi-level MCCM reflects the Stackelberg game between the moderator and decision-makers, in which two structural hole indices are used to obtain the weight of decision-makers and facilitate consensus-reaching, respectively. We analyze the Nash equilibrium strategy and design a particle swarm optimization algorithm to solve the bi-level MCCM. Furthermore, we implement the proposed bi-level MCCM on a social network generated from a real dataset. Subsequently, a detailed analysis of the implementation results shows the decisive role of social networks driving large-scale group consensus-reaching and reveals the relationship between position and benefit in the social network of decision-makers. Accordingly, management implications are given for LSGDM for both research and practice. • The Leiden algorithm is introduced to cluster the large-scale group. • A bi-level MCCM for LSGDM based on the structural hole theory is constructed. • Stackelberg equilibrium strategies in the proposed bi-level MCCM are analyzed. • A PSO-based algorithm is designed to solve the proposed bi-level MCCM. • Detailed implementation and analysis driven by a real dataset are exhibited. [ABSTRACT FROM AUTHOR]

Highlights • An AHPSort II method for sustainable supplier selection (SSS) is applied to IT2FSs. • Soft transitions in IT2FSs are used to sort suppliers into predefined classes. • A new way to determine representative points is developed. • Three types of criteria based on data availability and accuracy are used for evaluation. • Application of the methodology in SSS shows practical and theoretical usefulness. Abstract With increasing attention on protecting the environment and social involvement, the concept of sustainable development has been widely mentioned in various industries. A new management mode, sustainable supply chain management (SSCM), has come into being and has become a hot topic of discussion. As sustainable supplier selection is the most important issue in this mode, many multiple criteria decision-making (MCDM) methods for sustainable supplier selection have been proposed, though sometimes it is more useful the sorting of suppliers into classes that show the performance of such suppliers. Therefore, this paper proposes the use of the sorting method, AHPSort II, under a fuzzy environment with interval type-2 fuzzy sets (IT2FSs) and a new way of selecting representative points for inferring suppliers' priorities that will improve the management of unclear class assignments by softening transitions between classes facilitating the sustainable supplier selection. A significant reduction of comparisons compared to the AHP method together a higher precision of inferred priorities is occurred. This novel IT2FS sorting MCDM makes decisions become more in line with reality because of a better management of uncertainty and more accurate priorities. Finally, an application of the previous method to the selection of a sustainable material supplier is provided to show how the proposed method worked. [ABSTRACT FROM AUTHOR]

Type-2 fuzzy sets (T2FSs) exhibit evident merits when it comes to representing the complex and high uncertainty, which has been encountered in fuzzy optimization and multiple criteria decision making (MCDM) problems. Since T2FSs theory was proposed by Zadeh in 1975, then a series of theories and methods were investigated by more scholars. Type-2 fuzzy aggregation operators, contributing to the fundamental information fusion theory, have been paid more attention and applied to different areas during the last two decades. In this paper, a survey of type-2 fuzzy aggregation and application for MCDM is carried out. We first review some basic knowledge including definitions, operations, type reduction and ranking methods of T2FSs. Then the definitions and properties of some main aggregation operators are introduced. Furthermore, some application categories under type-2 fuzzy environment are given. Finally, we identify some existing shortcomings and point at future research directions on this topic.

Interval 2-tuple linguistic model is widely applied to group decision making owing to the representation capabilities.In order to deal with the problem of different labels (multi-granularity), an interval 2-tuple transformation function is developed, which is beneficial to information aggregation and fusion. In addition, a novel and flexible interval 2-tuple ranking function is introduced, which can obtain the ranking result in a single-step procedure. Based on the previous distance measures, the normalized generalized interval 2-tuple distance is proposed. Furthermore, an interval 2-tuple with the aid of TODIM method is introduced to select green suppliers. Finally, a sensitivity analysis is completed and a comparative analysis is carried out with interval 2-tuple TOPSIS and VIKOR methods to verify the validity of the proposed method.

Recently, sustainable supplier chain management (SSCM) has gained increasing attentions both from corporate and academic. A large number of multiple criteria group decision-making (MCGDM) methods for sustainable supplier selection have been developed. In this paper, considering that the interval type-2 fuzzy sets (IT2FSs) exhibit some interesting properties for handling uncertain information and high order imprecision, we integrate the ANP (analytical network process) method and the VIKOR (ViseKriterijumska Optimizacija I Kompromisno Resenje) method under interval type-2 fuzzy environment to solve supplier selection problem in SSCM. The proposed method consists of two steps. First, we obtain the weights of criteria via the ANP method. Then, based on the weights of criteria presented in step 1, a compromise solution will be proposed with the aid of VIKOR method. A numerical example is presented to show the decision process in detail. In addition, a comparative analysis with interval type-2 fuzzy ANP method and TOPSIS method is also presented to verify the validity of the proposed method.

Pythagorean fuzzy sets, originally proposed by Yager (IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS), pp 57–61, 2013), which are convenient to describe vagueness and impression in real-world problems, can be regarded as a novel extension of intuitionistic fuzzy sets. Generalized Maclaurin symmetric mean comes as an extension of classical Maclaurin symmetric mean. Their prominent feature is that they can both capture overall interrelationships and also focus on individual importance among the arguments. However, the generalized Maclaurin symmetric mean can only be considered for aggregating numeric information. In this paper, we investigate the generalized Maclaurin symmetric mean and further extend to Pythagorean fuzzy environment. We develop the Pythagorean fuzzy generalized Maclaurin symmetric mean (PFGMSM), the Pythagorean fuzzy weighted generalized Maclaurin symmetric mean (PFWGMSM), and discuss a variety of their desirable properties. To better understand the proposed parameterization operators, we provide an innovative way to extend the classical superiority and inferiority ranking (SIR) group decision model to Pythagorean fuzzy environment. Then, an approach formed with the aid of PFWGMSM and SIR to multiple attribute group decision-making with Pythagorean fuzzy information is developed. Finally, an illustrative example concerning supply chain financial risk decision-making is provided to verify the proposed method and demonstrate its effectiveness.

Interval type-2 fuzzy set (IT2FS) is a widely used tool for handling vagueness and imprecision in real-world problems. To aggregate the interval type-2 fuzzy information, some useful aggregation operators have been developed such as IT2-OWA, IT2-FWA, and IT2-Frank operators. In particular, some aggregation operators which can capture and reflect and interrelationships among aggregated arguments are intensively studied, among which Hamy mean (HM) is an important alternative. However, the traditional HM does not focus on fusion of fuzzy information and the weighted vector of the aggregated arguments. In this study, we extend the HM to accommodate interval type-2 fuzzy environment and show its application to multiple criteria decision making (MADM). In order to simplify the computing, we first define the concept of symmetric triangular interval type-2 fuzzy set and propose some operational laws. Motivated by the idea of HM operator, we develop the symmetric triangular interval type-2 fuzzy Hamy mean (STIT2FHM) operator for aggregating the interval type-2 fuzzy information. Some useful properties such as monotonicity, boundedness, and idempotencyare studied in detail. Furthermore, we discuss some special cases with respect to different parameter values of the STIT2FHM operator. For the situations where the input arguments have different importance, we further develop the weighted symmetric triangular interval type-2 fuzzy Hamy mean (WSTIT2FHM) operator to aggregate interval type-2 fuzzy information. Based on it, an approach to MCDM problems with symmetric triangular interval type-2 fuzzy information is developed. Finally, a real-world example concerning tourism recommender system is provided to illustrate the practicality and effectiveness of the proposed method.

Purpose – The purpose of this paper is to develop some 2-tuple linguistic aggregation operators based on Muirhead mean (MM), which is combined with multiple attribute group decision making (MAGDM) and applied the proposed MAGDM model for supplier selection under 2-tuple linguistic environment. Design/methodology/approach – The supplier selection problem can be regarded as a typical MAGDM problem, in which the decision information should be aggregated. In this paper, the authors investigate the MAGDM problems with 2-tuple linguistic information based on traditional MM operator. The MM operator is a well-known mean type aggregation operator, which has some particular advantages for aggregating multi-dimension arguments. The prominent characteristic of the MM operator is that it can capture the whole interrelationship among the multi-input arguments. Motivated by this idea, in this paper, the authors develop the 2-tuple linguistic Muirhead mean (2TLMM) operator and the 2-tuple linguistic dual Muirhead mean (2TLDMM) operator for aggregating the 2-tuple linguistic information, respectively. Some desirable properties and special cases are discussed in detail. Based on which, two approaches to deal with MAGDM problems under 2-tuple linguistic information environment are developed. Finally, a numerical example concerns the supplier selection problem is provided to illustrate the effectiveness and feasibility of the proposed methods. Findings – The results show that the proposed can solve the MAGDM problems within the context of 2-tuple linguistic information, in which the attributes are existing interaction phenomenon. Some 2-tuple aggregation operators based on MM have been developed. A case study of supplier selection is provided to illustrate the effectiveness and feasibility of the proposed methods. The results show that the proposed methods are useful to aggregate the linguistic decision information in which the attributes are not independent so as to select the most suitable supplier. Practical implications – The proposed methods can solve the 2-tuple linguistic MAGDM problem, in which the interactions exist among the attributes. Therefore, it can be used to supplier selection problems and other similar management decision problems. Originality/value – The paper develop some 2-tuple aggregation operators based on MM, and further present two methods based on the proposed operators for solving MAGDM problems. It is useful to deal with multiple attribute interaction decision-making problems and suitable to solve a variety of management decision-making applications. [ABSTRACT FROM AUTHOR]

AbstractIn this paper, we propose new methods to represent interdependence among alternative attributes and experts’ opinions by constructing Choquet integral using interval-valued intuitionistic fuzzy numbers. In the sequel, we apply these methods to solve the multiple attribute group decision-making (MAGDM) problems under interval-valued intuitionistic fuzzy environment. First, the concept of interval-valued intuitionistic fuzzy Choquet integral is defined, and some elementary properties are studied in detail. Next, an axiomatic system of interval-valued intuitionistic fuzzy measure is established by delivering a series of mathematical proofs. Then, with fuzzy entropy and Shapely-values in game theory, we propose the interval-valued intuitionistic fuzzy measure development methods in order to form the importance measure of attributes and correlation measure of the experts, respectively. Based on the results of theoretical analysis, a new method is proposed to handle the interval-valued intuitionistic fuzzy group decision making problems. A numerical example illustrates the procedure of the proposed methods and verifies the validity and effectiveness of our new proposed methods.

In this paper, we investigate the multiple-attribute decision-making (MADM) problems based on traditional Maclaurin symmetric mean operator operating under hesitant fuzzy environment. The Maclaurin symmetric mean (MSM) operator is a classical mean type aggregation operator and has strong modeling capability in modern information fusion theory, which has particular advantages for aggregating multi-dimension arguments. The prominent characteristic of the MSM operator is that it can capture the interrelationship among the multi-input arguments. Motivated by the idea of MSM operator, we develop the hesitant fuzzy Maclaurin symmetric mean (HFMSM) operator for aggregating the hesitant fuzzy information. Some desirable properties such as monotonicity, boundedness, idempotency are studied. Furthermore, we have discussed some special cases with respect to different parameter values of the HFMSM operator in detail. For the situations where the input arguments have different importance, we further develop the weighted hesitant fuzzy Maclaurin symmetric mean operator to aggregate hesitant fuzzy information. Based on which, an approach to MADM problems with hesitant fuzzy information is developed. Finally, a practical example with paper quality evaluation of sciencepaper online in China is provided to illustrate the practicality and effectiveness of the proposed method.

In this paper, we investigate a new method to handle multiple attribute group decision making (MAGDM) problems based on combined ranking value under interval type-2 fuzzy environment, in which all the attribute values provided by experts take the form of interval type-2 fuzzy sets (IT2FSs). We first introduce some basic concepts and related operational laws on IT2FSs. Then, we put forward three kinds of ranking value formulas to calculate the ranking value of IT2FSs based on arithmetic average (AA) operator, geometric average (GA) operator and harmonic average (HA) operator, respectively, and discuss some of its desirable properties. Based on these properties, we define the concept of combined ranking value and also further develop a new interval type-2 fuzzy entropy with trigonometric sine function to measure the uncertainty of the IT2FSs. By using the three types ranking value formulas and interval type-2 fuzzy entropy we proposed, a new approach based on the principle of combinatorial optimization with ranking-entropy and the least squares for determining attribute weight is given. Furthermore, a decision making procedure based on combined ranking value is given to select the best alternative(s). Finally, a simple practical example concerns that urban rail transit evaluation is provided to illustrate the practicality and effectiveness of the proposed method, and a comparative analysis is performed. [ABSTRACT FROM AUTHOR]

The portfolio allocation problem is a hot topic in modern economics and management science. It involves many immeasurable criteria and uncertainties. Given the advantage of interval type-2 fuzzy sets (IT2FSs) in modeling complexities and uncertainties, this study provides an integrated methodology to deal with portfolio allocation problem based on the multiple criteria group decision-making (MCGDM) method considering the consensus reaching process in an interval type-2 fuzzy environment. First, some new information measures for IT2FSs include the weighted mean, and the weighted semi-absolute deviation measures are defined. They are used to describe the return and risk of the portfolio allocation, respectively. Second, a two-stage MCGDM framework is constructed for portfolio allocation: one is to achieve the group consensus, and the other is to obtain the optimal portfolio ratios. Finally, an example on calculating the optimal portfolio ratios for four newly listed stocks in China is offered to elaborate on the performance of our approach. Sensitivity and comparative analyses are also given to show the effectiveness and advantages of the proposed method. [ABSTRACT FROM AUTHOR]

Fuzzy rule-based models and the extension of classical fuzzy models have been widely used in many domains. From a holistic perspective, regardless of the design methods and rules adopted in a fuzzy model, the determination of fuzzy sets is a pivotal issue. In the proposed methods, instead of traditional data clustering with no directional tendency, we introduce an optimization algorithm that can adjust the position of the prototypes of zero- and first-order fuzzy models to learn internal structure information from the data in the process of parameter identification. Furthermore, to build a granular fuzzy model, the prototypes are then scaled to more robust intervals by generating information granularity with specific semantics such that they split the whole output space. Particle swarm optimization algorithm is applied to adjust both the locations of the prototypes and the allocation of information granularity to improve the performance of the data-driven models. Experimental studies on synthetic and real-world datasets are provided to demonstrate the effectiveness of these methods. [ABSTRACT FROM AUTHOR]