Rule base simplification by using a similarity measure of fuzzy sets

Article type: Research Article

Authors: Rezaee, Babak

Affiliations: Department of Industrial Engineering, Bojnord University, Bojnord, Iran

Note: [] Corresponding author. Babak Rezaee, Department of Industrial Engineering, Bojnord University, P.O. Box 1339, Bojnord, Iran. Tel.: +98 584 228 6010; Fax: +98 584 241 0700; E-mail: [email protected]

Abstract: In fuzzy models, redundancy may be present in the form of similar fuzzy sets, especially in the construction of a fuzzy system from a set of given training examples. In this paper, a simple formula for calculating the degree of similarity of Trapezoidal membership functions is derived in order to merge similar membership functions and hence to obtain a more transparent rule-base with a minimum number of membership functions. A simplification algorithm by using the proposed similarity measure has been applied to fuzzy models of nonlinear functions approximation.

Keywords: Interpretability, fuzzy rule base simplification, distinguishability, similarity measure, trapezoidal membership functions

DOI: 10.3233/IFS-2012-0509

Journal: Journal of Intelligent & Fuzzy Systems, vol. 23, no. 5, pp. 193-201, 2012