Rule base reduction using conflicting and reinforcement measures

In this paper we present an innovative procedure to reduce the number of rules in a Mamdani rule-based fuzzy systems. First of all, we extend the similarity measure or degree between antecedent and consequent of two rules. Subsequently, we use the similarity degree to compute two new measures of conflicting and reinforcement between fuzzy rules. We apply these conflicting and reinforcement measures to suitably reduce the number of rules. Namely, we merge two rules together if they are redundant, i.e. if both antecedent and consequence are similar together, repeating this operation until no similar rules exist, obtaining a reduced set of rules. Again, we remove from the reduced set the rule with conflict with other, i.e. if antecedent are similar and consequence not; among the two, we remove the one characterized by higher average conflict with all the rules in the reduced set