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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. [ABSTRACT FROM AUTHOR]

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. [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]

The influence of socially responsible investment (SRI) has caused much attention from both institutional and individual investors in capital markets. SRI considers the corporate social responsibility (CSR) criteria of firms is becoming an emerging topic in economics and management. The aim of this paper is to develop a hybrid SRI portfolio selection model with multi-criteria decision making (MCDM) and multi-objective optimization problem (MOOP) techniques. First, a multi-dimensional evaluation criteria system containing fundamental financial indicators, CSR criteria, and stock market factors, is put forward for SRI to make the decision results more comprehensive and applicable. Second, a multi-stage MCDM decision mechanism including the affinity propagation clustering (APC) algorithm, the best-worst method (BWM), and the MULTIMOORA (Multi-Objective Optimization on the basis of a Ratio Analysis plus the full MULTIplicative form) is implemented. The APC algorithm is used for the reduction of financial indicators. The BWM is applied to determine the financial and CSR criteria weights. The MULTIMOORA method is integrated to derive the financial and CSR performance of the firms. Third, a multi-objective SRI portfolio selection model adding financial, CSR, and stock market performance is constructed, which serves as an extension of the classical mean-variance model. The compromise solution is utilized when solving the MOOP. Finally, a case study related to the medical stock investment is examined to recommend the optimal portfolio allocation for investors. Sensitivity and comparative analyses are performed to demonstrate the robustness, effectiveness, and superiority of the proposed methodology. • Develop a hybrid SRI portfolio selection model with MCDM and MOOP techniques • A multi-dimensional evaluation criteria system is put forward. • A multi-stage MCDM decision mechanism is implemented. • A multi-objective SRI portfolio selection model is constructed. • A case study related to the stock investment during the COVID-19 is examined. [ABSTRACT FROM AUTHOR]

In this paper, we investigate multiple attribute decision making (MADM) problems based on Frank triangular norms, in which the attribute values assume the form of hesitant fuzzy information. Firstly, some basic concepts of hesitant fuzzy set (HFS) and the Frank triangle norms are introduced. We develop some hesitant fuzzy aggregation operators based on Frank operations, such as hesitant fuzzy Frank weighted average (HFFWA) operator, hesitant fuzzy Frank ordered weighted averaging (HFFOWA) operator, hesitant fuzzy Frank hybrid averaging (HFFHA) operator, hesitant fuzzy Frank weighted geometric (HFFWG) operator, hesitant fuzzy Frank ordered weighted geometric (HFFOWG) operator, and hesitant fuzzy Frank hybrid geometric (HFFHG) operator. Some essential properties together with their special cases are discussed in detail. Next, a procedure of multiple attribute decision making based on the HFFHWA (or HFFHWG) operator is presented under hesitant fuzzy environment. Finally, a practical example that concerns the human resource selection is provided to illustrate the decision steps of the proposed method. The result demonstrates the practicality and effectiveness of the new method. A comparative analysis is also presented. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The eruption of COVID-19 at the beginning of 2020 has sounded the alarm, making experts pay more attention to public health emergency events. A suitable emergency response plan plays a vital role in handling emergency events. Therefore, this paper focuses on the evaluation of emergency response plans among a set of group in the comprehensive prospect, and an emergency decision making method integrated with the interval type-2 fuzzy information based on the third generation prospect theory (PT 3) and the extended MULTIMOORA method is proposed. Individuals express their preferences using some given linguistic terms set. Furthermore, considering the conflicts may occur in the group, a convergent iterative algorithm is designed for group consensus reaching. Then, the stochastic multi-criteria acceptability analysis (SMAA) method and the Borda Count (BC) method are generated to combine the results instead of the dominance theory in MULTIMOORA system. Finally, based on the background of the COVID-19 pandemic from Wuhan, a case study about the selection of emergency response plan and the corresponding sensitivity and comparative analysis are exhibited to explain the effectiveness of the proposed method. • A new fuzzy MCDA method to evaluate emergency response plans is proposed. • An integrated model based on PT3 and extended MULTIMOORA with IT2FSs is developed. • The proposed method considers CRP with an effectiveness iterative algorithm. • A case study of emergency response plans assessment on COVID-19 in Wuhan is presented. [ABSTRACT FROM AUTHOR]

Personnel selection is a critical enterprise strategic problem in knowledge-intensive enterprise. Fuzzy number which can be described as triangular (trapezoid) fuzzy number is an adequate way to assess the evaluation and weights for the alternatives. In that case, fuzzy TOPSIS, as a classic fuzzy multiple criteria decision making (MCDM) methods, has been applied in personnel selection problems. Currently, all the researches on this topic either apply crisp relative closeness but causing information loss, or employ fuzzy relative closeness estimate but with complicated computation to rank the alternatives. In this paper, based on Karnik–Mendel (KM) algorithm, we propose an analytical solution to fuzzy TOPSIS method. Some properties are discussed, and the computation procedure for the proposed analytical solution is given as well. Compared with the existing TOPSIS method for personnel selection problem, it obtains accurate fuzzy relative closeness instead of the crisp point or approximate fuzzy relative closeness estimate. It can both avoid information loss and keep computational efficiency in some extent. Moreover, the global picture of fuzzy relative closeness provides a way to further discuss the inner properties of fuzzy TOPSIS method. Detailed comparisons with approximate fuzzy relative closeness method are provided in personnel selection application. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a method based on Choquet integral is proposed to solve the interval intuitionistic fuzzy multiple attribute group decision making problems. Firstly, some concepts about interval intuitionistic fuzzy measure are defined, through the strict mathematical reasoning to prove the measure we proposed satisfying the axiomatic system of fuzzy measure. Then, on the basis of fuzzy measure and game theory, we propose two models to determine fuzzy measure based on interval intuitionistic fuzzy entropy and weight information matrix. By calculating the Shapely value to determine expert weights, we establish a linear programming model based on relative entropy to determine the fuzzy measure of attribute weights to reflect the interactive characteristics among the criteria, using the Choquet integral to aggregate the decision-making information. Finally, we give the process of decision making in details. [Copyright &y& Elsevier]

Owing to the rapidly changing customer preferences and demands, the e-commerce industry encounters various uncertainties and risks to enhance competitiveness. Quality function deployment (QFD) is a commonly used model, which can translate customer requirements (CRs) into products or service design requirements (DRs), to improve competitiveness by launching a new business. To measure the uncertainties and behavioral risk factors in e-commerce service design, we propose a new QFD model based on the Kano model and TOPSIS method by considering the behavior of experts with prospect theory under interval type-2 fuzzy linguistic environment. The categories of CRs are identified using the Kano model and the weights of CRs are determined dynamically according to the development stages of enterprises. The priorities of DRs are ranked using the extended TOPSIS method with prospect theory. A case study of China's e-commerce service design is used to show the application of the proposed QFD model. The prioritizing results show the flexibility of the proposed model on determining the weights of CRs and the priorities of DRs for enterprises at different development stages. • A quality function deployment model is proposed under linguistic environment. • Identify the attribute category of CRs using the interval type-2 fuzzy Kano model. • Determine the weights of CRs based on the development stage of enterprises. • Rank DRs by an extended TOPSIS method considering the behavioral factors. [ABSTRACT FROM AUTHOR]

In most existing multi-criteria group decision making (MCGDM) problems, the decision makers (DMs) are usually regarded as independent and DMs' psychological behaviors are rarely considered. However, in many cases, the opinions of DMs are likely to influence each other and the DMs often hold subjective bounded rationality in the decision making process. To address this issue, a linguistic distribution behavioral MCGDM model integrating extended generalized TODIM (an acronym in Portuguese of interactive and multi-criteria decision making) method and quantum decision theory is developed. First, linguistic distribution assessments considering the sample size information are used to gather the group linguistic evaluations, which can integrally depict the quantitative distribution and qualitative vagueness. Second, an extended generalized linguistic distribution TODIM method is presented to reflect the DMs' bounded rational behaviors. It is used to calculate the dominance of each alternative. Third, a quantum possibilistic aggregation framework is constructed to explore the interference effects among DMs' opinions. In this process, DMs' opinions are viewed as synchronously occurred wave functions that interfere with each other and influence the aggregated result. Finally, a case study is examined to recommend the optimal automobile for customers based on distributed online reviews in newcar.xcar.com and autohome.com. Three separate scenarios with conjunctive, neural, and disjunctive modes are considered respectively. The sensitivity analysis is given to show the effect of risk factors and interference factors. The parameters show to be dominant in the final best automobile recommendation. The comparisons with some existing methods confirm the validity and stability of the proposed MCGDM method. • Develop a novel linguistic distribution behavioral MCGDM model. • Integrate the generalized TODIM method and quantum decision theory. • Explore the interference effects among DMs' opinions in a quantum framework. • Apply the proposed model to the online automobile recommendation. [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]

In the last few years, emergencies have brought about catastrophic casualties and property loss. After an emergency, the emergency manager who is in charge of the rescue work has to identify an optimal rescue plan from several alternatives. Therefore, it is necessary to develop an effective method for selecting an optimal rescue plan to reduce the damages of emergencies. Usually, an emergency decision has three features: time urgency, incomplete information and potential severe results. While it is difficult to provide the accurate numerical evaluations with the incomplete information under limited time, the probabilistic linguistic term set (PLTS) is introduced to represent the opinions of emergency decision making panel (EDMP) in this paper. In this way, EDMP can provide suggestions with linguistic terms, and the manager can directly collect qualitative opinions in a short time. In addition, fault tree analysis (FTA) is used to evaluate the probabilities of potential severe results, and analysis network process (ANP) is adopted to derive the weights of criteria that determining the damages of potential severe results. Then, we can quantify the potential severe results of alternatives so as to choose the one with the minimum damages. In this study, we first attempt to integrate PLTS and FTA-ANP method to comprehensively consider the three features of emergency decision to select an optimal rescue plan. Finally, a case study is employed to verify the feasibility of the proposed method, and the comparisons and discussion are presented to show the rationality and novelty of this study. • The opinions of a group of experts are described by using PLTS. • The probabilities of the potential severe results are analyzed by FTA with PLTS. • The weights of criteria determining the damages are confirmed by ANP with PLTS. • The potential severe results of emergency are quantified by the FTA-ANP method. [ABSTRACT FROM AUTHOR]