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In the elicitation of decision makers' fuzzy and uncertain assessments, linguistic terms are natural and efficient as the preference modeling tools. Although the linguistic variables are available, they would not be operational without any detailed quantification. Motivated by the flexibility of information granularity, this paper develops information granules to represent linguistic terms in the form of intervals and interval type-2 fuzzy sets (IT2FSs) in best worst method (BWM). The development is aimed at minimizing inconsistency in the decision making (DM) process to ensure the rationality of the assessments provided by decision makers. Furthermore, the input and output based consistencies of BWM are considered. The granulation of entries of pairwise comparison vectors are the foundation of BWM to formulate an optimization problem where particle swarm optimization (PSO) algorithm serves as the optimization framework. Both individual and group decision making (GDM) scenarios are taken into consideration. For the GDM process, a performance index for measuring the group consensus is also proposed. Several examples and validity analysis are covered to illustrate the major ideas of this study. Finally, as a case study, a recommendation of the sequence of visiting tourist attractions in Wuhan and the corresponding comparative analysis are represented. • A granular computing-based method in BWM framework is proposed. • Construction of granular linguistic information to represent preference information of DMs is given. • A novel Euclidean distance function to measure the agreement among the group is proposed. • A case study of scenic spots recommendation in Wuhan with online reviews is exhibited. [ABSTRACT FROM AUTHOR]

Trust is crucial for purchasing decisions in social commerce. However, inexperienced users may not have a direct trust relation to experienced users in practice. Besides, users tend to give their trust degrees to others with linguistic labels rather than crisp values. To evaluate the trust degree for inexperienced users to experienced ones, we propose an interval type‐2 fuzzy trust evaluation model in this paper. Interval type‐2 fuzzy linguistic labels are used to represent trust degree among users. An interval type‐2 fuzzy Algebraic t‐norm is addressed to compute propagative trust degrees. Considering the effect of trust path length, the induced ordered weighted averaging (IOWA) operator is extended to aggregate the interval type‐2 fuzzy trust degrees obtained from multiple paths. In addition, the final interval type‐2 fuzzy trust degree is transferred into the corresponding linguistic label to help users make decisions more naturally. Finally, a case study in social commerce and a related comparison are given to verify the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

The Failure mode and effect analysis (FMEA) is an effective risk evaluation approach which has been widely used to assist in risk controlling in various workplaces. However, in practice, the conventional FMEA approach suffers from the drawbacks associated with the risk evaluation and priorization methods. In this paper, a novel risk priorization method for FMEA based on the extended MULTIMOORA (Multi-Objective Optimization by Ratio Analysis plus the Full Multiplicative Form) method is proposed. First, the interval type-2 fuzzy sets are applied to deal with the uncertainty of risk evaluation in FMEA. Second, the distance-based method is used to calculate the importance weight of each risk factor. Then, an extended MULTIMOORA method is presented to rank risk priority of each failure mode, in which the distance measure for interval type-2 fuzzy number is incorporated. Finally, a practical case in steel company is selected to illustrate the application and feasibility of the proposed approach. A comparative analysis is conducted to demonstrate the effectiveness of the developed risk priorization method. [ABSTRACT FROM AUTHOR]

Supplier selection is a key issue in supply chain management, which directly impacts the manufacturer's performance. The problem can be viewed as a multiple attribute group decision making (MAGDM) that concerns many conflicting evaluation attributes, both being of qualitative and quantitative nature. Due to the increasing complexity and uncertainty of socio-economic environment, some evaluations of attributes are not adequately represented by numerical assessments and type-1 fuzzy sets. In this paper, we develop some linear programming models with the aid of multidimensional analysis of preference (LINMAP) method to solve interval type-2 fuzzy MAGDM problems, in which the information about attribute weights is incompletely known, and all pairwise comparison judgments over alternatives are represented by IT2FSs. First, we introduce a new distance measure based on the centroid interval between the IT2FSs. Then, we construct the linear programming model to determine the interval type-2 fuzzy positive ideal solution (IT2PIS) and corresponding attributes weight vector. Based on it, an extended LINMAP method to solve MAGDM problem under IT2FSs environment is developed. Finally, a supplier selection example is provided to demonstrate the usefulness of the proposed method. [ABSTRACT FROM AUTHOR]

Type-2 fuzzy sets (T2FSs) have the advantage of representing higher-order uncertainty, they have demonstrated superior performance in several applications. In order to fully measure the uncertainty for T2FSs. In this study, several distribution characteristics of uncertainties within T2FSs are analyzed through type-1 fuzzy sets (T1FSs), and the axiomatic framework of fuzzy entropy and overall entropy of T2FSs is established as well. First, a new representation method for T2FSs is given. On this basis, the axiomatic definitions of fuzzy entropy for T1FSs and T2FSs are constructed by analyzing the distribution characteristics of fuzziness, and the construction theorems and basic properties of fuzzy entropy are studied. Further, the overall entropy of T2FSs is given, on this basis, a novel type-2 fuzzy entropy-based decision-making method is proposed, and applied to the selection of cold medicine through online reviews on AliHealth.cn. Finally, the feasibility and effectiveness of the developed definitions and methods are demonstrated by three comparative analyses. • A new mathematical expression of T2FSs is defined. • The axiomatic framework of fuzzy entropy of T2FSs is constructed. • The overall entropy of type-2 fuzzy information is defined. • A novel decision-making method based on overall entropy is developed. • A real application through online review is proposed. [ABSTRACT FROM AUTHOR]

Failure mode and effect analysis (FMEA) has been widely adopted to define, identity, and remove potential and recognized hazards. As an indicator in traditional FMEA, the risk priority number (RPN) is an effective tool for measuring risk and the calculation of RPN is also very simple. Nevertheless, there are many drawbacks in the conventional FMEA method. It is necessary to seek approaches that can make up for the deficiency of traditional FMEA method and strengthen assessment capability of ranking failure modes according to three relevant risk factors. This paper presents a way to combine interval type-2 fuzzy sets (IT2FSs) with evidential reasoning (ER) method, which is able to overcome some disadvantages of the conventional FMEA approach and deal with uncertainties more efficiently. First, we give a more precise expression of the risk factors in the form of IT2FSs and gain the relative weight of three risk factors. Second, one can judge the failure modes in relation to each risk factors with belief structures. Finally, the ER method is used to combine the belief structures under the weight of the three risk factors. To verify the feasibility of the method, an application for steam valve system is performed and the obtained results show the effectiveness of the method. • An interval type-2 fuzzy evidential reasoning method for FMEA is proposed. • Various assessments of team members are expressed by predefined linguistic terms. • A linear programming model to generate belief structure is developed. • An interval RPN is produced by fusing the information of three risk factors. • Demonstrate advantages of the proposed risk model with a steam valve system case. [ABSTRACT FROM AUTHOR]