This article provides a brief tour through the main fuzzy and linguistic decision-making trends, studies, methodologies, and models developed in the last 50 years. Fuzzy and linguistic decision-making approaches allow to address complex real-world decision problems where humans exhibit vagueness, imprecision, and/or use natural language to assess decision alternatives, criteria, etc. The aim of this article is threefold. First, the main fuzzy set theory and computing with words-based representation paradigms of decision information, with their different levels of expressive richness and complexity, are reviewed. Second, three core decision-making frameworks are examined: 1) multicriteria decision making; 2) group consensus-driven decision making; and 3) multiperson multicriteria decision making. Third, the article discusses new complex decision-making frameworks that have emerged in recent years, where decisions are guided by the “wisdom of the crowd”: their associated challenges are highlighted and considerations on much needed key guidelines for future research in the field are provided.

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Revisiting Fuzzy and Linguistic Decision Making: Scenarios and Challenges for Making Wiser Decisions in a Better Way

In the era of uncertain information everywhere, the Probabilistic Hesitant Fuzzy sets (PHFs), utilizing the possible numbers and its possible membership degrees to descript decision-makers’ behavior, has been brought about widespread attention. Scholars from all over the world applied numerous approaches in this environment since Probabilistic Hesitant Fuzzy sets (PHFs) has been come up with, and there are still untapped territories. The TODIM (TOmada deDecisao Iterativa Multicrite´rio) method is a common decision-making method which is based on the prospect theory (PT). Unlike the other multiple criteria decision making (MCDM) methods, the TODIM method think over the bounded rationality of decision makers to choose the optimal alternative according to the decision maker’s psychological reality. In this essay, we introduce the Extended TODIM Based on Cumulative Prospect Theory (CPT) for probabilistic hesitant fuzzy multiple attributes group decision-making (MAGDM). In addition, the entropy is applied to calculate the weights between attributes. Finally, the developed method is used to solve the decision-making case study. To test the reasonability of this new method, we utilize a numerical case to compare the extended TODIM method with other methods.

TODIM Method Based on Cumulative Prospect Theory for Multiple Attributes Group Decision Making Under Probabilistic Hesitant Fuzzy Setting

The paper aims to present an integrated approach to solve the decision-making problem under the probabilistic hesitant fuzzy information (PHFI) features, which is an extension of the hesitant fuzzy set. The considered PHFI not only allows multiple opinions, but also associates occurrence probability to each opinion, which increases the reliability of the information. Motivated by these features of PHFI, an approach is presented to solve the decision problem with partial known information about the attribute and expert weights. In addition, an algorithm for finding some missing values in the preference information is presented and stated their properties. Afterward, the Hamy mean operator has been used to aggregate the different collective information into a single one. Also, we presented a COPRAS method to the PHFI for ranking the given alternatives. The presented algorithm has been demonstrated through a case study of cloud vendor selection and its validity has been revealed by comparing the approach results with the several existing algorithm results.

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An integrated decision-making COPRAS approach to probabilistic hesitant fuzzy set information

Facing with a sea of fuzzy information, decision makers always feel it difficult to select the optimal alternatives. Probabilistic hesitant fuzzy sets (PHFs) utilize the possible numbers and the possible membership degrees to describe the behavior of the decision makers. though this environment has been introduced to solve problems using different methods, this circumstance can still be explored by using different method. This paper’ s aim is to develop the MABAC (Multi-Attributive Border Approximation area Comparison) decision-making method which based on cumulative prospect theory (CPT) in probabilistic hesitant fuzzy environment to handle multiple attributes group decision making (MAGDM) problems. Then the weighting vector of attributes can be calculated by the method of entropy. Then, in order to show the applicability of the proposed method, it is validated by a case study for buying a house. Finally, through comparing the outcome of comparative analysis, we conclude that this designed method is acceptable.

CPT-MABAC-Based multiple attribute group decision making method with probabilistic hesitant fuzzy information

New ranking model with evidence theory under probabilistic hesitant fuzzy context and unknown weights

As an important extension of fuzzy number, the probabilistic hesitant fuzzy element (PHFE) shows the flexibility of decision makers in expressing hesitant information in multi-criteria decision-making (MCDM) processes. Accordingly, numerous research findings have been obtained since PHFE introduction. However, a few important issues in PHFE utilization remain to be addressed. This study introduces the French organization Rangement Et Synthese De Ronnees Relationnelles’ (ORESTE) approach for MCDM with probabilistic hesitant fuzzy information. First, the limitations of normalized PHFE (NPHFE), Euclidean distance, and several operations in previous studies are discussed. Subsequently, an algorithm is designed to derive the new NPHFE. A new Euclidean distance and several operations are developed on the basis of the proposed NPHFE. Second, the ORESTE approach is extended to probabilistic hesitant fuzzy environments. Lastly, the problem of selecting best research topic is presented to demonstrate that the proposed approach is effective. A comparative study with other approaches is conducted with identical illustrative example.

An ORESTE approach for multi-criteria decision-making with probabilistic hesitant fuzzy information

As a generalized fuzzy number, probabilistic hesitant fuzzy element (PHFE) improves the flexibility for decision makers in expressing hesitant information, and it has been receiving increased attention. This study develops a multi-criteria decision-making (MCDM) approach that considers consensus reaching among decision makers with probabilistic hesitant fuzzy information. To obtain this aim, first, a new approach to derive normalized PHFE (NPHFE) is proposed to overcome the shortcomings in previous studies. Subsequently, a new Euclidean distance and some operations related to PHFEs are developed based on the new proposed NPHFEs. At the same time, the effectiveness and rationality of the new proposed approaches are discussed. Second, a consensus index of group with PHFEs is presented, which based on the proposed Euclidean distance of decision-makers’ evaluation information on all the criteria. Third, if the consensus level of the group does not reach the expect threshold value, an iteration algorithm is designed to improve its consensus level. Moreover, the proof of the convergence of the proposed algorithm is provided to verify its effectiveness, and a MCDM approach based on group consensus is proposed. Finally, the most comprehensive candidate selection problems are provided to demonstrate the effectiveness of the proposed MCDM approach. And a comparative study with other methods is conducted with the same illustrative example.

A consensus-based approach for multi-criteria decision making with probabilistic hesitant fuzzy information

Hesitant fuzzy preference relations (HFPRs) have been widely applied in multicriteria decision-making (MCDM) for their ability to efficiently express hesitant information. To address the situation where HFPRs are necessary, this paper develops several decision-making models integrating HFPRs with the best worst method (BWM). First, consistency measures from the perspectives of additive/multiplicative consistent hesitant fuzzy best worst preference relations (HFBWPRs) are introduced. Second, several decision-making models are developed in view of the proposed additive/multiplicatively consistent HFBWPRs. The main characteristic of the constructed models is that they consider all the values included in the HFBWPRs and consider the same and different compromise limit constraints. Third, an absolute programming model is developed to obtain the decision-makers’ objective weights utilizing the information of optimal priority weight vectors and provides the calculation of decision-makers’ comprehensive weights. Finally, a framework of the MCDM procedure based on hesitant fuzzy BWM is introduced, and an illustrative example in conjunction with comparative analysis is provided to demonstrate the feasibility and efficiency of the proposed models.

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Approaches for multicriteria decision-making based on the hesitant fuzzy best–worst method


 To address the situation where the incomplete hesitant fuzzy preference relation (IHFPR) is necessary, this paper develops decision-making models based on decision makers’ satisfaction degree with IHFPR. First, the consistency measures from the perspectives of additive and multiplicative consistent IHFPR are defined based on the relationships between the IHPFRs and their corresponding priority weight vector, respectively. Second, two decision-making models are developed in view of the proposed additive and multiplicative consistency measures. The main characteristic of the constructed model sarethey taking into account the decision makers’ satisfaction degree. The objective functions of the models are developed by maximizing the parameter of satisfaction degree. Third, a square programming model is developed to obtain the decision makers’ weights byutilizing the optimal priority weight vectors information, the solution of the model is obtained by solving the partial derivatives ofLagrange function.Finally, a procedure for multi-criteria decision-making (MCDM) problems with IHFPRs is given, and an illustrative example in conjunction with comparative analysis is used to demonstrate the proposed models are feasible and efficiency for practical MCDM problems.

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Decision-Making Models Based on Satisfaction Degree with Incomplete Hesitant Fuzzy Preference Relation

Abstract To address the situation where the multi-criteria decision making (MCDM) has problems with hesitant fuzzy preference relations (HFPRs), this paper develops a group decision making method considering the additive consistency and consensus simultaneously. First, a new normalized method for HFPRs is developed to address the situation where the evaluation information has different number of elements. Second, for improving the unacceptable consistent HFPRs, an algorithm is designed to derive acceptable consistent HFPRs. The main characteristic of the design algorithm is that the values that need to be revised are identified first, and then design the local adjustment process. Third, an algorithm is developed to obtain a group of normalized HFPRs (NHFPRs), considering the additive consistency of HFPRs. Fourth, for improving the individual consistency and group consensus simultaneously, an algorithm is designed to obtain a group of HFPRs with acceptable consistency and consensus. Finally, the method of determining the decision makers’ weights and a procedure for MCDM problems with HFPRs are given. An illustrative example in conjunction with comparative analysis is used to demonstrate the proposed method which is feasible and efficient for practical MCDM problems. 

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Qiongxia Chen

Papers

An ORESTE approach for multi-criteria decision-making with probabilistic hesitant fuzzy information

A consensus-based approach for multi-criteria decision making with probabilistic hesitant fuzzy information

Approaches for multicriteria decision-making based on the hesitant fuzzy best–worst method

Decision-Making Models Based on Satisfaction Degree with Incomplete Hesitant Fuzzy Preference Relation

Group decision making method with hesitant fuzzy preference relations based on additive consistency and consensus