Abstract and Applied Analysis

A New Similarity Measure between Intuitionistic Fuzzy Sets and Its Application to Pattern Recognition

Yafei Song, Xiaodan Wang, Lei Lei, and Aijun Xue

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Abstract

As a generation of ordinary fuzzy set, the concept of intuitionistic fuzzy set (IFS), characterized both by a membership degree and by a nonmembership degree, is a more flexible way to cope with the uncertainty. Similarity measures of intuitionistic fuzzy sets are used to indicate the similarity degree between intuitionistic fuzzy sets. Although many similarity measures for intuitionistic fuzzy sets have been proposed in previous studies, some of those cannot satisfy the axioms of similarity or provide counterintuitive cases. In this paper, a new similarity measure and weighted similarity measure between IFSs are proposed. It proves that the proposed similarity measures satisfy the properties of the axiomatic definition for similarity measures. Comparison between the previous similarity measures and the proposed similarity measure indicates that the proposed similarity measure does not provide any counterintuitive cases. Moreover, it is demonstrated that the proposed similarity measure is capable of discriminating difference between patterns.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 384241, 11 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412277175

Digital Object Identifier
doi:10.1155/2014/384241

Mathematical Reviews number (MathSciNet)
MR3256245

Zentralblatt MATH identifier
07022277

Citation

Song, Yafei; Wang, Xiaodan; Lei, Lei; Xue, Aijun. A New Similarity Measure between Intuitionistic Fuzzy Sets and Its Application to Pattern Recognition. Abstr. Appl. Anal. 2014 (2014), Article ID 384241, 11 pages. doi:10.1155/2014/384241. https://projecteuclid.org/euclid.aaa/1412277175


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