Aggregation Operators and Distance Measures for Probabilistic q-Rung Orthopair Hesitant Fuzzy Sets and Their Applications

2021 ◽  
Author(s):  
Wenjing Yin ◽  
Tingting Zheng ◽  
Longmei Li
Keyword(s):  
Fuzzy Sets ◽  
Aggregation Operators ◽  
Distance Measures ◽  
Hesitant Fuzzy Sets

scholarly journals Novel Parameterized Distance Measures on Hesitant Fuzzy Sets with Credibility Degree and Their Application in Decision-Making

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 557 ◽  
Author(s):  
Jiaru Li ◽  
Fangwei Zhang ◽  
Qiang Li ◽  
Jing Sun ◽  
Janney Yee ◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Cardinal Number ◽  
Decision Makers ◽  
Distance Measures ◽  
Hesitant Fuzzy Set ◽  
Hesitant Fuzzy Sets ◽  
The Subject ◽  
The Relationship

The subject of this study is to explore the role of cardinality of hesitant fuzzy element (HFE) in distance measures on hesitant fuzzy sets (HFSs). Firstly, three parameters, i.e., credibility factor, conservative factor, and a risk factor are introduced, thereafter, a series of novel distance measures on HFSs are proposed using these three parameters. These newly proposed distance measures handle the relationship between the cardinal number and the element values of hesitant fuzzy set well, and are suitable to combine subjective and objective decision-making information. When using these functions, decision makers with different risk preferences are allowed to give different values for these three parameters. In particular, this study transfers the hesitance degree index to a credibility of the values in HFEs, which is consistent with people’s intuition. Finally, the practicability of the newly proposed distance measures is verified by two examples.

scholarly journals DUAL HESITANT FUZZY AGGREGATION OPERATORS

2015 ◽  
Vol 22 (2) ◽  
pp. 194-209 ◽  
Author(s):  
Dejian YU ◽  
Wenyu ZHANG ◽  
George HUANG
Keyword(s):  
Human Resources ◽  
Fuzzy Sets ◽  
Geometric Mean ◽  
Arithmetic Mean ◽  
Aggregation Operators ◽  
Fuzzy Arithmetic ◽  
Hesitant Fuzzy Sets ◽  
Numerical Example ◽  
Fuzzy Environment ◽  
Fuzzy Aggregation

Dual hesitant fuzzy sets (DHFSs) is a generalization of fuzzy sets (FSs) and it is typical of membership and non-membership degrees described by some discrete numerical. In this article we chiefly concerned with introducing the aggregation operators for aggregating dual hesitant fuzzy elements (DHFEs), including the dual hesitant fuzzy arithmetic mean and geometric mean. We laid emphasis on discussion of properties of newly introduced operators, and give a numerical example to describe the function of them. Finally, we used the proposed operators to select human resources outsourcing suppliers in a dual hesitant fuzzy environment.

On Extending Power-Geometric Operators to Interval-Valued Hesitant Fuzzy Sets and Their Applications to Group Decision Making

2016 ◽  
Vol 15 (05) ◽  
pp. 1055-1114 ◽  
Author(s):  
Sheng-Hua Xiong ◽  
Zhen-Song Chen ◽  
Yan-Lai Li ◽  
Kwai-Sang Chin
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Individual Decision ◽  
Hesitant Fuzzy Sets ◽  
Variable Power ◽  
Interval Valued

Developing aggregation operators for interval-valued hesitant fuzzy sets (IVHFSs) is a technological task we are faced with, because they are specifically important in many problems related to the fusion of interval-valued hesitant fuzzy information. This paper develops several novel kinds of power geometric operators, which are referred to as variable power geometric operators, and extends them to interval-valued hesitant fuzzy environments. A series of generalized interval-valued hesitant fuzzy power geometric (GIVHFG) operators are also proposed to aggregate the IVHFSs to model mandatory requirements. One of the important characteristics of these operators is that objective weights of input arguments are variable with the change of a non-negative parameter. By adjusting the exact value of the parameter, the influence caused by some “false” or “biased” arguments can be reduced. We demonstrate some desirable and useful properties of the proposed aggregation operators and utilize them to develop techniques for multiple criteria group decision making with IVHFSs considering the heterogeneous opinions among individual decision makers. Furthermore, we propose an entropy weights-based fitting approach for objectively obtaining the appropriate value of the parameter. Numerical examples are provided to illustrate the effectiveness of the proposed techniques.

Novel Multi-criteria Decision-making Approaches Based on Hesitant Fuzzy Sets and Prospect Theory

2016 ◽  
Vol 15 (03) ◽  
pp. 621-643 ◽  
Author(s):  
Juan-Juan Peng ◽  
Jian-Qiang Wang ◽  
Xiao-Hui Wu
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Prospect Theory ◽  
Hausdorff Distance ◽  
Comparison Method ◽  
Distance Measures ◽  
Preference Ranking ◽  
Multi Criteria Decision Making ◽  
The Novel ◽  
Hesitant Fuzzy Sets

Hesitant fuzzy sets (HFSs), an extension of fuzzy sets, are considered to be useful in solving decision making problems where decision makers are unable to choose between several values when expressing their preferences. The purpose of this paper is to develop two hesitant fuzzy multi-criteria decision making (MCDM) methods based on prospect theory (PT). First, the novel component-wise ordering method for two hesitant fuzzy numbers (HFNs) is defined; however, this method does not consider the length of the two HFNs. Second, by utilizing the directed Hausdorff distance between two imprecise point sets, the generalized hesitant Hausdorff distance is developed, which overcomes the shortcomings of the existing distance measures. Third, based on the proposed comparison method and distance, as well as PT, the extended TODIM and Preference Ranking Organization Method for Enrichment Evaluations (PROMETHEE) approaches are developed in order to solve MCDM problems with hesitant fuzzy information. Finally, a practical example is provided to illustrate the pragmatism and effectiveness of the proposed approaches. Sensitivity and comparison analyses are also conducted using the same example. The findings indicate that the proposed methods do not require complicated computation procedures, yet still yield a reasonable and credible solution.

Distance measures for higher order dual hesitant fuzzy sets

2017 ◽  
Vol 37 (2) ◽  
pp. 1784-1806 ◽  
Author(s):  
Jianjian Chen ◽  
Xianjiu Huang ◽  
Jing Tang
Keyword(s):  
Fuzzy Sets ◽  
Higher Order ◽  
Distance Measures ◽  
Hesitant Fuzzy Sets

scholarly journals EXTENDED HESITANT FUZZY SETS

2017 ◽  
Vol 22 (1) ◽  
pp. 100-121 ◽  
Author(s):  
Bin ZHU ◽  
Zeshui XU
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Close Relationships ◽  
Information Loss ◽  
Intuitionistic Fuzzy Sets ◽  
Decision Makers ◽  
Distance Measures ◽  
Hesitant Fuzzy Sets ◽  
Information Loss Problem

Hesitant fuzzy sets (HFSs) are a useful tool to manage situations in which the decision makers (DMs) hesitate about several possible values for the membership to assess a variable, alternative, etc. However, HFSs have the information loss problem and cannot identify different DMs, which interferes with the application of HFSs in decision making. To overcome these limitations, we develop the extended hesitant fuzzy sets (EHFSs) in this paper. As an extension of HFSs, EHFSs have close relationships with existing fuzzy sets including intuitionistic fuzzy sets (IFSs), fuzzy multisets (FMSs), type-2 fuzzy sets (T2FSs), dual hesitant fuzzy sets (DHFSs), and especially HFSs. We propose a concept of extended hesitant fuzzy elements (EHFEs), then study the basic operations and the desirable properties of EHFEs in detail. Some extended hesitant distance measures are developed to illustrate their advantages comparing with the existing hesitant distance measures. To extend EHFSs to decision making, we combine the proposed distance measures with the Dempster-Shafer belief structure.

New distance measures on hesitant fuzzy sets based on the cardinality theory and their application in pattern recognition

2016 ◽  
Vol 22 (4) ◽  
pp. 1237-1245 ◽  
Author(s):  
Fangwei Zhang ◽  
Shuyan Chen ◽  
Jianbo Li ◽  
Weiwei Huang
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Distance Measures ◽  
Hesitant Fuzzy Sets

scholarly journals A Decision Support Model for Hotel Recommendation Based on the Online Consumer Reviews Using Logarithmic Spherical Hesitant Fuzzy Information

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 432
Author(s):  
Aziz Khan ◽  
Shougi S. Abosuliman ◽  
Saleem Abdullah ◽  
Muhammad Ayaz
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Fuzzy Information ◽  
Hesitant Fuzzy Sets ◽  
Consumer Reviews ◽  
Online Consumer Reviews ◽  
Operational Laws ◽  
Online Consumer

Spherical hesitant fuzzy sets have recently become more popular in various fields. It was proposed as a generalization of picture hesitant fuzzy sets and Pythagorean hesitant fuzzy sets in order to deal with uncertainty and fuzziness information. Technique of Aggregation is one of the beneficial tools to aggregate the information. It has many crucial application areas such as decision-making, data mining, medical diagnosis, and pattern recognition. Keeping in view the importance of logarithmic function and aggregation operators, we proposed a novel algorithm to tackle the multi-attribute decision-making (MADM) problems. First, novel logarithmic operational laws are developed based on the logarithmic, t-norm, and t-conorm functions. Using these operational laws, we developed a list of logarithmic spherical hesitant fuzzy weighted averaging/geometric aggregation operators to aggregate the spherical hesitant fuzzy information. Furthermore, we developed the spherical hesitant fuzzy entropy to determine the unknown attribute weight information. Finally, the design principles for the spherical hesitant fuzzy decision-making have been developed, and a practical case study of hotel recommendation based on the online consumer reviews has been taken to illustrate the validity and superiority of presented approach. Besides this, a validity test is conducted to reveal the advantages and effectiveness of developed approach. Results indicate that the proposed method is suitable and effective for the decision process to evaluate their best alternative.

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