Learning Flexible Structured Linguistic Fuzzy Rules for Mamdani Fuzzy Systems

One significant challenge in building fuzzy systems for complex problems is the "curse of dimensionality". For the sake of a reduced size of the knowledge base, some rules with incomplete premise structures covering larger areas of the input domain are often desirable. This paper presents a genetic algorithm based approach to searching for suitable antecedents of rules under which specific fuzzy consequences can be recommended. The rule premises are coded in a flexible way allowing for presence as well as absence of an input variable in them, in combination with a certain class of input and output fuzzy sets. On the other hand, a consistency index is introduced to give a numerical evaluation of the coherence among individual rules. This index is incorporated into the fitness function of the genetic algorithm to search for a set of optimal rule premises yielding not only good problem solving performances but also little conflict in the rule base. The effectiveness of our work is demonstrated through experiment results on controlling an inverted pendulum.