Integrating Antonyms in Fuzzy Inferential Systems via Anti-membership

  • Scott DickEmail author
  • Peter Sussner
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1000)


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.


Fuzzy inferential systems Linguistic variables Antonyms Lattice theory 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.University of AlbertaEdmontonCanada
  2. 2.University of CampinasCampinasBrazil

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