scholarly journals A Consistency Check Method for Trusted Hesitant Fuzzy Sets with Confidence Levels Based on a Distance Measure

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Huimin Xiao ◽  
Meiqi Wang ◽  
Xiaoning Xi
Keyword(s):  
Fuzzy Sets ◽  
Distance Measure ◽  
Consistency Check ◽  
Hesitant Fuzzy Sets ◽  
Numerical Examples ◽  
Confidence Levels ◽  
Check Method ◽  
The Difference

This paper proposes a consistency check method for hesitant fuzzy sets with confidence levels by employing a distance measure. Firstly, we analyze the difference between each fuzzy element and its corresponding attribute comprehensive decision value and then obtain a comprehensive distance measure for each attribute. Subsequently, by taking the relative credibility as the weight, we assess the consistency of hesitant fuzzy sets. Finally, numerical examples are put forward to verify the effectiveness and reliability of the proposed method.

scholarly journals A Dynamic Distance Measure of Picture Fuzzy Sets and Its Application

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 436
Author(s):  
Ruirui Zhao ◽  
Minxia Luo ◽  
Shenggang Li
Keyword(s):  
Fuzzy Sets ◽  
Distance Measure ◽  
Distance Measures ◽  
Numerical Comparison ◽  
Mathematical Tool ◽  
Practical Applications ◽  
Fuzzy Point ◽  
Point Operator ◽  
The Difference ◽  
Picture Fuzzy Sets

Picture fuzzy sets, which are the extension of intuitionistic fuzzy sets, can deal with inconsistent information better in practical applications. A distance measure is an important mathematical tool to calculate the difference degree between picture fuzzy sets. Although some distance measures of picture fuzzy sets have been constructed, there are some unreasonable and counterintuitive cases. The main reason is that the existing distance measures do not or seldom consider the refusal degree of picture fuzzy sets. In order to solve these unreasonable and counterintuitive cases, in this paper, we propose a dynamic distance measure of picture fuzzy sets based on a picture fuzzy point operator. Through a numerical comparison and multi-criteria decision-making problems, we show that the proposed distance measure is reasonable and effective.

scholarly journals A Theoretical Development of Distance Measure for Intuitionistic Fuzzy Numbers

2010 ◽  
Vol 2010 ◽  
pp. 1-25 ◽  
Author(s):  
Debashree Guha ◽  
Debjani Chakraborty
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Numbers ◽  
Distance Measure ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Theoretical Development ◽  
Numerical Examples ◽  
Intuitionistic Fuzzy Numbers ◽  
Metric Properties ◽  
Intuitionistic Fuzzy

The objective of this paper is to introduce a distance measure for intuitionistic fuzzy numbers. Firstly the existing distance measures for intuitionistic fuzzy sets are analyzed and compared with the help of some examples. Then the new distance measure for intuitionistic fuzzy numbers is proposed based on interval difference. Also in particular the type of distance measure for triangle intuitionistic fuzzy numbers is described. The metric properties of the proposed measure are also studied. Some numerical examples are considered for applying the proposed measure and finally the result is compared with the existing ones.

Some Measures of Picture Fuzzy Sets and Their Application

2017 ◽  
Vol 3 (2) ◽  
pp. 35
Author(s):  
Nguyen Van Dinh ◽  
Nguyen Xuan Thao
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Distance Measure ◽  
Intuitionistic Fuzzy Set ◽  
Dissimilarity Measure ◽  
Intuitionistic Fuzzy ◽  
Picture Fuzzy Set ◽  
The Difference ◽  
Picture Fuzzy Sets

To measure the difference of two fuzzy sets (FSs) / intuitionistic sets (IFSs), we can use the distance measure and dissimilarity measure between fuzzy sets/intuitionistic fuzzy set. Characterization of distance/dissimilarity measure between fuzzy sets/intuitionistic fuzzy set is important as it has application in different areas: pattern recognition, image segmentation, and decision making. Picture fuzzy set (PFS) is a generalization of fuzzy set and intuitionistic set, so that it have many application. In this paper, we introduce concepts: difference between PFS-sets, distance measure and dissimilarity measure between picture fuzzy sets, and also provide  the formulas for determining these values. We also present an application of dissimilarity measures in the sample recognition problems, can also be considered a decision-making problem.

scholarly journals New Distance Measure for Atanassov’s Intuitionistic Fuzzy Sets and Its Application in Decision Making

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 429 ◽  
Author(s):  
Di Ke ◽  
Yafei Song ◽  
Wen Quan
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Distance Measure ◽  
Intuitionistic Fuzzy Set ◽  
Research Area ◽  
Intuitionistic Fuzzy Sets ◽  
Intuitionistic Fuzzy ◽  
The Difference ◽  
Atanassov’S Intuitionistic Fuzzy Sets

The intuitionistic fuzzy set introduced by Atanassov has greater ability in depicting and handling uncertainty. Intuitionistic fuzzy measure is an important research area of intuitionistic fuzzy set theory. Distance measure and similarity measure are two complementary concepts quantifying the difference and closeness of intuitionistic fuzzy sets. This paper addresses the definition of an effective distance measure with concise form and specific meaning for Atanassov’s intuitionistic fuzzy sets (AIFSs). A new distance measure for AIFSs is defined based on a distance measure of interval values and the transformation from AIFSs to interval valued fuzzy sets. The axiomatic properties of the new distance measure are mathematically investigated. Comparative analysis based in numerical examples indicates that the new distance measure is competent to quantify the difference between AIFSs. The application of the new distance measure is also discussed. A new method for multi-attribute decision making (MADM) is developed based on the technique for order preference by similarity to an ideal solution method and the new distance measure. Numerical applications indicate that the developed MADM method can obtain reasonable preference orders. This shows that the new distance measure is effective and rational from both mathematical and practical points of view.

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.

Note on distance measure of hesitant fuzzy sets

2015 ◽  
Vol 321 ◽  
pp. 103-115 ◽  
Author(s):  
Deqing Li ◽  
Wenyi Zeng ◽  
Yibin Zhao
Keyword(s):  
Fuzzy Sets ◽  
Distance Measure ◽  
Hesitant Fuzzy Sets
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