Why um and u*log(u) Are the Most Effective Nonlinear Functions in Fuzzy Clustering: Theoretical Explanation of the Empirical Fact

Authors

Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow
Yuchi Kanzawa, Shibaura Institute of TechnologyFollow

Publication Date

4-1-2025

Comments

Technical Report: UTEP-CS-25-11

Abstract

In fuzzy clustering, we need to have non-linear functions of the membership degrees. Different nonlinear functions have been tried. Empirical evidence shows that for fuzzy clustering, the most effective nonlinear functions are um and u*log(u). In this paper, we provide a theoretical explanation for this empirical fact.