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

Fuzzy random variables have been introduced by Purl and Ralescu as an exten sion of random sets. In this paper, we first introduce a real-valued genera lized measure of the "relative variation" (or inequality) associated with a fuzzy random variable. This measure is inspired in Csiszar's S-divergence, and extends to fuzzy random variables many well-known inequality indices. To guarantee certain relevant properties of this measure, we have to distin guish two main families of measures which will be characterized. Then, the fundamental properties are derived, and an outstanding measure in each fami ly is separately examined on the basis of an additive decomposition propert y and an additive decomposability one. Finally, two examples illustrate the application of the study in this paper. (C) 2001 Elsevier Science Inc. hll rights reserved.