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• 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]

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]