Natural Invariance Explains Empirical Success of Specific Membership Functions, Hedge Operations, and Negation Operations

Authors

Julio Urenda, The University of Texas at El PasoFollow
Orsoly Csiszár, Óbuda UniversityFollow
Gábor Csiszár, University of StuttgartFollow
József Dombi, University of SzegedFollow
György Eigner, Óbuda UniversityFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

6-2020

Comments

Technical Report: UTEP-CS-20-58

To appear in: Proceedings of the Annual Conference of the North American Fuzzy Information Processing Society NAFIPS'2020, Redmond, Washington, August 20-22, 2020.

Abstract

Empirical studies have shown that in many practical problems, out of all symmetric membership functions, special distending functions work best, and out of all hedge operations and negation operations, fractional linear ones work the best. In this paper, we show that these empirical successes can be explained by natural invariance requirements.