Integrating Antonyms in Fuzzy Inferential Systems via Anti-membership

Abstract

Numerous authors have proposed extending fuzzy inferential systems to include the antonyms in fuzzy rules. To date, however, those efforts require significant changes to the nature of a linguistic variable, directly implying substantial additional computation. We propose a new mechanism for incorporating antonyms into fuzzy rules, based on allowing negative-valued memberships along with two new union and intersection operations developed by Dick et al. We prove that these operations form a total ordering over [−1,1], and then show how they integrate antonyms into fuzzy rules seamlessly and require little additional computation.