Abstract
This paper analyzes the counterintuitive behaviors of transformed fuzzy number (FN)- based similarity measures between intuitionistic fuzzy sets (IFSs). Among these transformed FN-based similarity measures, Chen and Chang’s similarity measure (2015) is a novel one. An algorithm of computing Chen and Chang’s similarity measure is proposed. We analyze the counterintuitive behaviors of Chen and Chang’s similarity measure for seven general test problems and four test problems with three inclusive IFSs. The results indicate that there are six counterintuitive test problems for Chen and Chang’s similarity measure.
Highlights
Fuzzy sets (FSs) theory, proposed by Zadeh [1], has successfully been applied in various fields.As a generalization of FSs, intuitionistic fuzzy sets (IFSs) proposed by Atanassov [2] are characterized by a membership function and a non-membership function.A similarity measure between two IFSs represents alignment of the two sets
The existing similarity measures between two IFSs can be classified into four categories: one minus distance between two vectors [11,15,19,20,21,22], transformed fuzzy numbers (FNs) [9,13], centroid points [12,14], and others [17,18]
FN-based similarity measures, Zhang and Yu’s similarity measure [9] has the drawback of the division by zero problem, so this paper focuses on Chen and Chang’s similarity measure [13]
Summary
Fuzzy sets (FSs) theory, proposed by Zadeh [1], has successfully been applied in various fields. Many papers have been dedicated to problems connected with the similarity measures between two IFSs and research on this area is still carrying on [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22]. The other one is the four special test problems with three inclusive IFSs. The organization of this paper is as follows.
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