A generalized real-valued measure of the inequality associated with a fuzzy random variable

摘要

Fuzzy random variables have been introduced by Puri and Ralescu as an extension of random sets. In this paper, we first introduce a real-valued generalized measure of the "relative variation" (or inequality) associated with a fuzzy random variable. This measure is inspired in Csiszar' s f-divergence, and extends to fuzzy random variables many well-known inequality indices. To guarantee certain relevant properties of this measure, we have to distinguish two main families of measures which will be charac- terized.