research-article

An evidential view of similarity measure for Atanassov’s intuitionistic fuzzy sets

Authors: Yafei Song, Xiaodan Wang, Lei Lei, Wen Quan, Wenlong HuangAuthors Info & Claims

Journal of Intelligent & Fuzzy Systems, Volume 31, Issue 3

Pages 1653 - 1668

https://doi.org/10.3233/JIFS-151859

Published: 01 January 2016 Publication History

Abstract

In this paper, the construction of similarity measures for Atanassov’s intuitionistic fuzzy sets (AIFSs) is considered from the view of evidence theory. We define similarity measures for AIFSs in the framework of Dempster–Shafer evidence theory. The proposed similarity measures are applied to deal with pattern recognition and multiple criteria decision making problems. First, existing similarity measures for AIFSs are critically reviewed. Then we introduce the transformation from AIFSs to basic probability assignments (BPAs) in evidence theory. Based on Jousselme’s distance measure and cosine similarity measure between BPAs, two similarity measures between AIFSs are proposed. A composite similarity measure is constructed following the proof of properties related to our proposed similarity measures. Then, we use some contrastive examples to illustrate that the proposed similarity measure between AIFSs can overcome the drawbacks of existing similarity measures. Finally, we apply the proposed similarity measures between AIFSs to deal with pattern recognition and multiple criteria decision making problems. It is demonstrated that our proposed similarity measures can provide compatible results compared to those results obtained based on previous measures.

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Cited By

Gao XPan LDeng Y(2022)Cross entropy of mass function and its application in similarity measureApplied Intelligence10.1007/s10489-021-02890-652:8(8337-8350)Online publication date: 1-Jun-2022
https://dl.acm.org/doi/10.1007/s10489-021-02890-6
Luo MZhang YFu L(2021)A New Similarity Measure for Picture Fuzzy Sets and Its Application to Multi-Attribute Decision MakingInformatica10.15388/21-INFOR45232:3(543-564)Online publication date: 1-Jan-2021
https://dl.acm.org/doi/10.15388/21-INFOR452
Huang CMi XKang B(2021)Basic probability assignment to probability distribution function based on the Shapley value approachInternational Journal of Intelligent Systems10.1002/int.2245636:8(4210-4236)Online publication date: 18-May-2021
https://dl.acm.org/doi/10.1002/int.22456
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An evidential view of similarity measure for Atanassov’s intuitionistic fuzzy sets

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cover image Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology

Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology Volume 31, Issue 3

2016

864 pages

ISSN:1064-1246

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IOS Press and the authors. All rights reserved.

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IOS Press

Netherlands

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Published: 01 January 2016

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Cited By

Gao XPan LDeng Y(2022)Cross entropy of mass function and its application in similarity measureApplied Intelligence10.1007/s10489-021-02890-652:8(8337-8350)Online publication date: 1-Jun-2022
https://dl.acm.org/doi/10.1007/s10489-021-02890-6
Luo MZhang YFu L(2021)A New Similarity Measure for Picture Fuzzy Sets and Its Application to Multi-Attribute Decision MakingInformatica10.15388/21-INFOR45232:3(543-564)Online publication date: 1-Jan-2021
https://dl.acm.org/doi/10.15388/21-INFOR452
Huang CMi XKang B(2021)Basic probability assignment to probability distribution function based on the Shapley value approachInternational Journal of Intelligent Systems10.1002/int.2245636:8(4210-4236)Online publication date: 18-May-2021
https://dl.acm.org/doi/10.1002/int.22456
Zhang HSong YLei LQi Z(2020)A new method to measure the knowledge amount of Atanassov’s intuitionistic fuzzy sets2020 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)10.1109/FUZZ48607.2020.9177541(1-7)Online publication date: 19-Jul-2020
https://dl.acm.org/doi/10.1109/FUZZ48607.2020.9177541

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