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Abstract and Applied Analysis
Volume 2014, Article ID 384241, 11 pages
Research Article

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

School of Air and Missile Defense, Air Force Engineering University, Xi’an 710051, China

Received 22 April 2014; Accepted 13 August 2014; Published 27 August 2014

Academic Editor: Maria A. Ragusa

Copyright © 2014 Yafei Song et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.