Entropy measures for hesitant fuzzy sets and their application in multi-criteria decision-making

2016 ◽  
Vol 31 (1) ◽  
pp. 673-685 ◽  
Author(s):  
Cuiping Wei ◽  
Feifei Yan ◽  
Rosa M. Rodríguez
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Multi Criteria Decision Making ◽  
Hesitant Fuzzy Sets ◽  
Entropy Measures

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.

The fuzzy cross-entropy for intuitionistic hesitant fuzzy sets and their application in multi-criteria decision-making

2014 ◽  
Vol 46 (13) ◽  
pp. 2335-2350 ◽  
Author(s):  
Juan-juan Peng ◽  
Jian-qiang Wang ◽  
Xiao-hui Wu ◽  
Hong-yu Zhang ◽  
Xiao-hong Chen
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Cross Entropy ◽  
Multi Criteria Decision Making ◽  
Hesitant Fuzzy Sets

scholarly journals Modelling Uncertainties in Multi-Criteria Decision Making using Distance Measure and TOPSIS for Hesitant Fuzzy Sets

2017 ◽  
Vol 7 (2) ◽  
pp. 103-109 ◽  
Author(s):  
Ismat Beg ◽  
Tabasam Rashid
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Distance Measure ◽  
Fuzzy Data ◽  
Multi Criteria Decision Making ◽  
Ideal Solution ◽  
Hesitant Fuzzy Sets ◽  
New Approach ◽  
Order Preference ◽  
Modelling Uncertainties

Abstract A notion for distance between hesitant fuzzy data is given. Using this new distance notion, we propose the technique for order preference by similarity to ideal solution for hesitant fuzzy sets and a new approach in modelling uncertainties. An illustrative example is constructed to show the feasibility and practicality of the new method.

An extension of ELECTRE to multi-criteria decision-making problems with multi-hesitant fuzzy sets

2015 ◽  
Vol 307 ◽  
pp. 113-126 ◽  
Author(s):  
Juan-juan Peng ◽  
Jian-qiang Wang ◽  
Jing Wang ◽  
Li-Jun Yang ◽  
Xiao-hong Chen
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Multi Criteria Decision Making ◽  
Hesitant Fuzzy Sets

scholarly journals On Some Knowledge Measures of Intuitionistic Fuzzy Sets of Type Two with Application to MCDM

2020 ◽  
Vol 20 (1) ◽  
pp. 3-20 ◽  
Author(s):  
Surender Singh ◽  
Sumita Lalotra ◽  
Abdul Haseeb Ganie
Keyword(s):  
Decision Making ◽  
Comparative Study ◽  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Fuzzy Entropy ◽  
Multi Criteria Decision Making ◽  
Intuitionistic Fuzzy ◽  
Knowledge Measure ◽  
Intuitionistic Fuzzy Entropy ◽  
Entropy Measures

AbstractTo overcome the certain limitations of Intuitionistic Fuzzy Sets (IFSs), the notion of Intuitionistic Fuzzy Sets of Second Type (IFSST) was introduced. IFSST is a modified version of IFS for handling some problems in a reasonable manner. Type two Intuitionistic Fuzzy entropy (IFSST-entropy) measures the amount of ambiguity/uncertainty present in an IFSST. In the present paper, we introduce the concept of dual measure of IFSST-entropy, i.e., IFSST-knowledge measure. We develop some IFSST-knowledge measures and prove some of their properties. We also show the superiority of the proposed IFSST-knowledge measures through comparative study. Further, we demonstrate the application of the proposed knowledge measures in Multi-Criteria Decision-Making (MCDM).

scholarly journals Convex Aggregation Operators and Their Applications to Multi-Hesitant Fuzzy Multi-Criteria Decision-Making

Information ◽  
2018 ◽  
Vol 9 (9) ◽  
pp. 207 ◽  
Author(s):  
Ye Mei ◽  
Juanjuan Peng ◽  
Junjie Yang
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Choquet Integral ◽  
Convex Combination ◽  
Weighted Average ◽  
Aggregation Operators ◽  
Multi Criteria Decision Making ◽  
Hesitant Fuzzy Sets ◽  
Novel Approach ◽  
Ordered Weighted Average

Hesitant fuzzy sets (HFSs), which were generalized from fuzzy sets, constrain the membership degree of an element to be a set of possible values between zero and one; furthermore, if two or more decision-makers select the same value, it is only counted once. However, a situation where the evaluation value is repeated several times differs from one where the value appears only once. Multi-hesitant fuzzy sets (MHFSs) can deal effectively with a case where some values are repeated more than once in a MHFS. In this paper, the novel convex combination of multi-hesitant fuzzy numbers (MHFNs) is introduced. Some aggregation operators based on convex operation, such as generalized multi-hesitant fuzzy ordered weighted average (GMHFOWA) operator, generalized multi-hesitant fuzzy hybrid weighted average (GMHFHWA) operator, generalized multi-hesitant fuzzy prioritized weighted average (GMHFPWA) operator and generalized multi-hesitant fuzzy Choquet integral weighted average (GMHFCIWA) operator, are developed and corresponding properties are discussed in detail. Then, based on the proposed aggregation operators, a novel approach for multi-criteria decision-making (MCDM) problem is proposed for ranking alternatives. Finally, an example is provided to verify the developed approach and demonstrate its validity and feasibility and the study is supported by a sensitivity analysis and a comparison analysis.

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