Learning rules for hierarchical fuzzy logic systems using Wu & mendel IF-THEN rules quality measures

Abstract

This paper focuses on problems related to learning rules using numerical data for the Hierarchical Fuzzy Logic Systems (HFLS) described in [12]. Using hierarchical structure of Fuzzy Logic Systems (FLS) complex problems could be divided into subproblems with smaller dimensions. “Hierarchical” means that fuzzy sets produced as output of one of fuzzy logic systems are then processed as an input of another one as the sets of auxiliary variables. The main problem is to learn a rulebase with numerical data, which does not contain any data for those auxiliary variables. Learning rules for FLS in short could be accomplished by using many different approaches, building one, complex rulebase using all available input and output variables for complex problems. Our learning method based on the Wang & Mendel (W&M) method adopted for the HFLS with selective activation of unit FLS were introduced in [13]. The main scope of this paper is to extend our method applying quality measures of IFTHEN rules in the sense of Wu & Mendel (Wu&M) to remove conflicting rules. The proposal presented in this paper operates on a type-1 HFLS, built with the fuzzy logic systems (in the sense of Mamdani). An example of single-player games, i.e. where the “enemy” is controlled by agents is used. Two new problems are briefly introduced.