Hesitant Fuzzy Sets and Hesitant Fuzzy Preference Relations

AbstractAs an enhanced version of probabilistic hesitant fuzzy sets and dual hesitant fuzzy sets, probabilistic dual hesitant fuzzy sets (PDHFSs) combine probabilistic information with the membership degree and non-membership degree, which can describe decision making information more reasonably and comprehensively. Based on PDHFSs, this paper investigates the approach to group decision making (GDM) based on incomplete probabilistic dual hesitant fuzzy preference relations (PDHFPRs). First, the definitions of order consistency and multiplicative consistency of PDHFPRs are given. Then, for the problem that decision makers (DMs) cannot provide the reasonable associated probabilities of probabilistic dual hesitant fuzzy elements (PDHFEs), the calculation method of the associated probability is given by using an optimal programming model. Furthermore, the consistency level for PDHFPRs is tested according to the weighted consistency index defined by the risk attitude of DMs. In addition, a convergent iterative algorithm is proposed to enhance the unacceptable consistent PDHFPRs’ consistency level. Finally, a GDM approach with incomplete PDHFPRs is established to obtain the ranking of the alternatives. The availability and rationality of the proposed decision making approach are demonstrated by analyzing the impact factors of haze weather.

Download Full-text

Evaluation of the product quality of the online shopping platform using t-spherical fuzzy preference relations

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-202930 ◽

2021 ◽

pp. 1-18

Author(s):

Choonkil Park ◽

Shahzaib Ashraf ◽

Noor Rehman ◽

Saleem Abdullah ◽

Muhammad Aslam

Keyword(s):

Decision Making ◽

Product Quality ◽

Fuzzy Sets ◽

Online Shopping ◽

Score Function ◽

Decision Makers ◽

Preference Relations ◽

Fuzzy Preference Relations ◽

Fuzzy Preference

As a generalization of Pythagorean fuzzy sets and picture fuzzy sets, spherical fuzzy sets provide decision makers more flexible space in expressing their opinions. Preference relations have received widespread acceptance as an efficient tool in representing decision makers’ preference over alternatives in the decision-making process. In this paper, some new preference relations are investigated based on the spherical fuzzy sets. Firstly, the deficiency of the existing operating laws is elaborated in detail and three cases are described to identify the accuracy of the proposed operating laws in the context of t-spherical fuzzy environment. Also, a novel score function is proposed to obtain the consistent value in ranking of the alternatives. The backbone of this research, t-spherical fuzzy preference relation, consistent t-spherical fuzzy preference relations, incomplete t-spherical fuzzy preference relations, consistent incomplete t-spherical fuzzy preference relations, and acceptable incomplete t-spherical fuzzy preference relations are established. Additionally, some ranking and selection algorithms are established using the proposed novel score function and preference relations to tackle the uncertainty in real-life decision-making problems. Finally, evaluation of the product quality of the online shopping platform problem is demonstrated to show the applicability and reliability of proposed technique.

Download Full-text

Decision support model with Pythagorean fuzzy preference relations and its application in financial early warnings

Complex & Intelligent Systems ◽

10.1007/s40747-021-00390-1 ◽

2021 ◽

Author(s):

Wenying Wu ◽

Zhiwei Ni ◽

Feifei Jin ◽

Ying Li ◽

Juan Song

Keyword(s):

Decision Making ◽

Decision Support ◽

Fuzzy Sets ◽

Group Decision Making ◽

Group Decision ◽

Decision Support Model ◽

Preference Relations ◽

Fuzzy Preference Relations ◽

Fuzzy Preference ◽

Support Model

AbstractPythagorean fuzzy sets (PFSs) retain the advantages of intuitionistic fuzzy sets (IFSs), while PFSs portray 1.57 times more information than IFSs. In addition, Pythagorean fuzzy preference relations (PFPRs), as a generalization of intuitionistic fuzzy preference relations (IFPRs), are more flexible and applicable. The objective of this paper is to propose a novel decision support model for solving group decision-making problems in a Pythagorean fuzzy environment. First, we define the concepts of ordered consistency and multiplicative consistency for PFPRs. Then, aiming at the group decision-making problem of multiple PFPRs, a consistency improving model is constructed to improve the consistency of group preference relations. Later, a consensus reaching model is developed to reach the degree of group consensus. Furthermore, a decision support model with PFPRs is established to derive the normalized weights and output the final result. Holding these features, this paper builds a decision support model with PFPRs based on multiplicative consistency and consensus. Finally, the described method is validated by an example of financial risk management, and it is concluded that the solvency of a company is an important indicator that affects the financial early warning system.

Download Full-text

POLITICAL REPRESENTATION: PERSPECTIVE FROM FUZZY SYSTEMS THEORY

New Mathematics and Natural Computation ◽

10.1142/s1793005707000690 ◽

2007 ◽

Vol 03 (02) ◽

pp. 153-163 ◽

Cited By ~ 3

Author(s):

HANNU NURMI ◽

JANUSZ KACPRZYK

Keyword(s):

Social Choice ◽

Fuzzy Sets ◽

Systems Theory ◽

Fuzzy Systems ◽

Political Representation ◽

Preference Relations ◽

Fuzzy Preference Relations ◽

Transitive Preference ◽

Theory Of Fuzzy Sets ◽

Fuzzy Preference

The theory of fuzzy sets has been applied to social choice primarily in the context where one is given a set of individual fuzzy preference relations and the aim is to find a non-fuzzy choice set of winners or best alternatives. In this article, we discuss the problem of composing multi-member deliberative bodies starting again from a set of individual fuzzy preference relations. We outline methods of aggregating these relations into a measure of how well each candidate represents each voter in terms of the latter's preferences. Our main goal is to show how the considerations discussed in the context of individual non-fuzzy complete and transitive preference relations can be extended into the domain of fuzzy preference relations.

Download Full-text

Decision making based on intuitionistic fuzzy preference relations with additive approximate consistency

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-200200 ◽

2020 ◽

Vol 39 (3) ◽

pp. 4041-4058

Author(s):

Fang Liu ◽

Xu Tan ◽

Hui Yang ◽

Hui Zhao

Keyword(s):

Decision Making ◽

Decision Makers ◽

Real Interval ◽

Preference Relations ◽

Intuitionistic Fuzzy ◽

Proposed Model ◽

Fuzzy Preference Relations ◽

Novel Concept ◽

Fuzzy Weights ◽

Fuzzy Preference

Intuitionistic fuzzy preference relations (IFPRs) have the natural ability to reflect the positive, the negative and the non-determinative judgements of decision makers. A decision making model is proposed by considering the inherent property of IFPRs in this study, where the main novelty comes with the introduction of the concept of additive approximate consistency. First, the consistency definitions of IFPRs are reviewed and the underlying ideas are analyzed. Second, by considering the allocation of the non-determinacy degree of decision makers’ opinions, the novel concept of approximate consistency for IFPRs is proposed. Then the additive approximate consistency of IFPRs is defined and the properties are studied. Third, the priorities of alternatives are derived from IFPRs with additive approximate consistency by considering the effects of the permutations of alternatives and the allocation of the non-determinacy degree. The rankings of alternatives based on real, interval and intuitionistic fuzzy weights are investigated, respectively. Finally, some comparisons are reported by carrying out numerical examples to show the novelty and advantage of the proposed model. It is found that the proposed model can offer various decision schemes due to the allocation of the non-determinacy degree of IFPRs.

Download Full-text