Interpolative fuzzy reasoning method based on the incircle of a generalized triangular fuzzy number

Article type: Research Article

Authors: Alzubi, Maen^{; *} | Kovacs, Szilveszter

Affiliations: Department of Information Technology, University of Miskolc, H-3515 Miskolc, Hungary

Correspondence: [*] Corresponding author. Maen Alzubi, Department of Information Technology, University of Miskolc, H-3515 Miskolc, Hungary. E-mail: [email protected].

Abstract: Fuzzy Rule Interpolation (FRI) is an important technique for implementing inference with sparse fuzzy rule-bases. Even if a given observation has no overlap with the antecedent of any rule from the rule-base, FRI may still conclude a conclusion. This paper introduces a new method called “Incircle FRI” for fuzzy interpolation which is based on the incircle of a triangular fuzzy number. The suggested method is defined for triangular CNF fuzzy sets, for a single antecedent universe and two surrounding rules from the rule-base. The paper also extends the suggested “Incircle FRI” to trapezoidal, and hexagonal shaped fuzzy sets by decomposing their shapes to multiple triangulars. The generated conclusion is also a CNF fuzzy set. The performance of the suggested method is evaluated based on numerical examples and a comprehensive comparison to other current FRI methods.

Keywords: Fuzzy interpolative reasoning, sparse fuzzy rule-based systems, incircle triangular fuzzy numbers, incircle FRI method

DOI: 10.3233/JIFS-191660

Journal: Journal of Intelligent & Fuzzy Systems, vol. 39, no. 1, pp. 709-729, 2020