Some preference relations based on q‐rung orthopair fuzzy sets

2019 ◽  
Vol 34 (11) ◽  
pp. 2920-2936 ◽  
Author(s):  
Hongxu Li ◽  
Songyi Yin ◽  
Yang Yang
Keyword(s):  
Fuzzy Sets ◽  
Preference Relations

On the Rationality of Some Crisp Choice Functions Based on Strongly Complete Fuzzy Pre-Orders

2015 ◽  
Vol 11 (01) ◽  
pp. 103-113 ◽  
Author(s):  
Siméon Fotso ◽  
Louis Aimé Fono
Keyword(s):  
Fuzzy Sets ◽  
Choice Functions ◽  
Preference Relations ◽  
Natural Computation ◽  
Weak Preference ◽  
Choice Sets

Barrett, Pattanaik and Salles [Fuzzy Sets and Systems 34 (1990) 197–212] introduced nine alternative rules for generating exact choice sets from fuzzy weak preference relations (FWPR) and four rationality properties. They showed that, when preferences are fuzzy pre-orders, most of these alternative rules (preference-based choice functions or PCFs) violate at least two rationality properties. Following in the same direction, Fotso and Fono [New Mathematics and Natural Computation 8 (2012) 257–272] characterized these PCFs and analyzed their consistency in the cases of strongly complete fuzzy pre-orders and crisp complete pre-orders. In this paper, based on results of the two previous papers, we determine to what extend the PCFs are rational with respect to the structure of the underlying relation. More specifically, for each of the nine alternative rules violating a given rationality property, we determine respectively crisp pre-orders and strongly complete fuzzy pre-orders for which the PCF satisfies the property.

scholarly journals An Approach for Achieving Consistency for Symmetric Trapezoidal Interval Type-2 Fuzzy Sets

2019 ◽  
Vol 2019 ◽  
pp. 1-16
Author(s):  
Jiuping Xu ◽  
Kang Xu
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Preference Relation ◽  
Mapping Method ◽  
Linguistic Terms ◽  
Actual Case ◽  
Preference Relations ◽  
Interval Type

Interval type-2 fuzzy sets (IT2 FSs) are powerful tools for dealing with linguistic information in decision making. However, there is a dearth of research regarding the consistency of preference relations based on IT2 FSs. In this paper, symmetric IT2 FSs and IT2 additive preference relations are defined, whilst at the same time a mapping method is proposed to convert IT2 numbers into the corresponding linguistic terms based on the ranking values for IT2 FSs, and some properties for symmetric IT2 FSs are proved. Then, we discuss the process for achieving consistency for IT2 additive preference relations. An algorithm is developed for the IT2 additive preference relation process for achieving consistency, and some desired algorithmic properties are proved. Finally, an actual case study is used in order to demonstrate the effectiveness of the proposed approach.

scholarly journals A new group decision making approach based on incomplete probabilistic dual hesitant fuzzy preference relations

2021 ◽  
Author(s):  
Juan Song ◽  
Zhiwei Ni ◽  
Feifei Jin ◽  
Ping Li ◽  
Wenying Wu
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Group Decision Making ◽  
Group Decision ◽  
Membership Degree ◽  
Hesitant Fuzzy Sets ◽  
Preference Relations ◽  
Fuzzy Preference Relations ◽  
The Impact ◽  
Fuzzy Preference

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.

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

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.

scholarly journals PROBABILITY-HESITANT FUZZY SETS AND THE REPRESENTATION OF PREFERENCE RELATIONS

2018 ◽  
Vol 24 (3) ◽  
pp. 1029-1040 ◽  
Author(s):  
Bin ZHU ◽  
Zeshui XU
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Preference Relation ◽  
Decision Makers ◽  
Stochastic Method ◽  
Hesitant Fuzzy Sets ◽  
Fuzzy Preference Relation ◽  
Preference Relations ◽  
Hesitant Fuzzy Preference Relation ◽  
Consensus Index

Probability interpretations play an important role in understanding decision makers’ (DMs) behaviour in decision making. In this paper, we extend hesitant fuzzy sets to probability-hesitant fuzzy sets (P-HFSs) to enhance their modeling ability by taking DMs’ probabilistic preferences into consideration. Based on P-HFSs, we propose the concept of probability-hesitant fuzzy preference relation (P-HFPR) to collect the preferences. We then develop a consensus index to measure the consensus degrees of P-HFPR, and a stochastic method to improve the consensus degrees. All these results are essential for further research on P-HFSs.

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

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.

POLITICAL REPRESENTATION: PERSPECTIVE FROM FUZZY SYSTEMS THEORY

2007 ◽  
Vol 03 (02) ◽  
pp. 153-163 ◽  
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.

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