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.
Highlights
Since it was proposed by Zadeh [1], the theory of fuzzy set (FS) has achieved great success due to its capability of handling uncertainty
Considering the outcome of the analysis presented by Bustince and Burillo [5], which concluded that the intuitionistic fuzzy sets and the vague sets are similar, Chen [29] proposed the first similarity measure for Intuitionistic fuzzy set (IFS) defined as SC (A, B) = 1 − ∑ni=1 (μA (xi) − VA (xi)) − (μB (xi) − VB (xi)) . 2n (5)
We propose an alternative approach to medical diagnosis using the newly defined similarity measure
Summary
Since it was proposed by Zadeh [1], the theory of fuzzy set (FS) has achieved great success due to its capability of handling uncertainty. Xu [18] introduced a series of similarity measures for IFSs and applied them to multiple attribute decision making problem based on intuitionistic fuzzy information. Xia and Xu [6] proposed a series of distance measures based on the intuitionistic fuzzy point operators In addition to these studies, some works have been interested in relationships between distance measure, similarity measure, and entropy of IFSs. Zeng and Guo [21] investigated the relationship among the normalized distance, the similarity measure, the inclusion measure, and the entropy of interval-valued fuzzy sets. Zhang and Yu [24] presented a new distance (or similarity) measure based on interval comparison, where the IFSs were, respectively, transformed into the symmetric triangular fuzzy numbers.
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