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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References
Antonie, M.-L., Zaiane, O.R.: An associative classifier based on positive and negative rules. In: ACM Data Mining and Knowledge Discovery (2004)
Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87–96 (1986)
Branson, J.S., Lilly, J.H.: Incorporation, characterization, and conversion of negative rules into fuzzy inference systems. IEEE Trans. Fuzzy Syst. 9, 253–268 (2001)
De Soto, A.R.: On automorphisms, synonyms, antonyms in fuzzy set theory. In: ITHURS (1996)
de Soto, A.R., Trillas, E.: On antonym and negate in fuzzy logic. Int. J. Intell. Syst. 14, 295–303 (1999)
Dick, S., Yager, R., Yazdanbakhsh, O.: On pythagorean and complex fuzzy set operations. IEEE Trans. Fuzzy Syst. 24, 1009–1021 (2016)
Garcia-Honrado, I., Trillas, E.: An essay on the linguistic roots of fuzzy sets. Inf. Sci. 181, 4061–4074 (2011)
Guadarrama, S., Ruiz-Mayor, A.: Approximate robotic mapping from sonar data by modeling perceptions with antonyms. Inf. Sci. 180, 4164–4188 (2010)
Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice Hall PTR, Upper Saddle River (1995)
Lawry, J.: A methodology for computing with words. Int. J. Approximate Reasoning 28, 51–89 (2001)
Novak, V.: Antonyms and linguistic qualifiers in fuzzy logic. Fuzzy Sets Syst. 124, 335–351 (2001)
Osgood, C.E., Suci, G.J., Tannenbaum, P.H.: The Measurement of Meaning. University of Illinois Press, Chicago (1957)
Smith, N.K., Larsen, J.T., Chartrand, T.L., Cacioppo, J.T.: Being bad isn’t always good: affective context moderates the attention bias toward negative information. J. Pers. Soc. Psychol. 90, 210–220 (2006)
Tizhoosh, H.: Opposite fuzzy sets with applications in image processing. In: IFSA-EUSFLAT, Lisbon, Portugal (2009)
Trillas, E., Moraga, C., Guadarrama, S., Cubillo, S., Castineira, E.: Computing with antonyms. In: Nikravesh, M., et al. (eds.) Forging New Frontiers: Fuzzy Pioneers I, pp. 133–153. Springer, Berlin (2007)
Trillas, E., Riera, T.: Towards a representation of synonyms and antonyms by fuzzy sets. BUSEFAL 5, 42–68 (1980)
Vaish, A., Grossmann, T., Woodward, A.: Not all emotions are created equal: the negativity bias in social-emotional development. Psych. Bull. 134, 383–403 (2008)
Zhang, W.-R.: (Yin) (Yang) bipolar fuzzy sets. In: IEEE International Conference on Fuzzy Systems, Anchorage, AK, USA (1998)
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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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