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.
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Dick, S., Sussner, P. (2019). Integrating Antonyms in Fuzzy Inferential Systems via Anti-membership. In: Kearfott, R., Batyrshin, I., Reformat, M., Ceberio, M., Kreinovich, V. (eds) Fuzzy Techniques: Theory and Applications. IFSA/NAFIPS 2019 2019. Advances in Intelligent Systems and Computing, vol 1000. Springer, Cham. https://doi.org/10.1007/978-3-030-21920-8_22
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DOI: https://doi.org/10.1007/978-3-030-21920-8_22
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