Why Cauchy Membership Functions: Efficiency

Authors

Javier Viana, University of CincinnatiFollow
Stephan Ralescu, University of CincinnatiFollow
Kelly Cohen, University of CincinnatiFollow
Anca Ralescu, University of CincinnatiFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

6-1-2021

Comments

Technical Report: UTEP-CS-21-58b

Published in Advances in Artificial Intelligence and Machine Learning, 2021, Vol. 1, No. 1, pp. 81-88.

Abstract

Fuzzy techniques depend heavily on eliciting meaningful membership functions for the fuzzy sets used. Often such functions are obtained from data. Just as often they are obtained from experts knowledgable of the domain and the problem being addressed. However, there are cases when neither is possible, for example because of insufficient data, or unavailable experts. What functions should one choose and what should guide such choice? This paper argues in favor of using Cauchy membership functions, thus named because their expression is similar to that of the Cauchy distributions. The paper provides a theoretical explanation for this choice.