Similarity measures of interval-valued fuzzy sets

Article type: Research Article

Authors: Li, Yingfang^{a; b} | Qin, Keyun^b | He, Xingxing^{b; *} | Meng, Dan^a

Affiliations: [a] School of Economics Information Engineering, Southwestern University of Finance and Economics, Chengdu, Sichuan, PR China | [b] Department of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan, PR China

Correspondence: [*] Correspondence author: X.X. He, Department of Mathematics, Southwest Jiaotong University, Chengdu 610031, Sichuan, PR China. Tel.: +86 13808003779; Fax: +86 28 87600764; xinghe010@gmail.com

Abstract: Interval-valued fuzzy set (briefly, IVFS) is a generalization of fuzzy set that may better model imperfect information. Similarity measure is a useful tool for determining the similarity degree between two fuzzy concepts. In this paper, the definition of similarity measure of IVFSs is presented. Three approaches to constructing similarity measures of IVFSs are proposed. Based on the approaches, three computation formulae for calculating the similarity degree between IVFSs are obtained. The properties of similarity measures of IVFSs are examined as a whole.

Keywords: Interval-valued fuzzy set, fuzzy set, similarity measure, fuzzy equivalence

DOI: 10.3233/IFS-141492

Journal: Journal of Intelligent & Fuzzy Systems, vol. 28, no. 5, pp. 2113-2125, 2015