Analytical formulas for similarity, possibility and distinguishability measures of Cauchy type fuzzy sets with comparison to Gaussian fuzzy sets

Abstract

This paper provides general analytical formulas for similarity and distinguishabilty measures of fuzzy sets of Cauchy type membership functions. A generalized analytical formula between similarity and possibility measures has also been obtained. A comparison with the case of Gaussian fuzzy sets ensures interesting monotonic characteristic charts for Cauchy type fuzzy sets compared with those of Gaussian fuzzy sets. This result represents a significant guide for building interpretable fuzzy models by adopting suitable forms of fuzzy sets as linguistic values based on their characteristic charts.