Fuzzy random variables revisited

Abstract

Reviews the concept of a fuzzy random variable, its expected value, and limit theorems for sequences of fuzzy random variables. The author points out shortcomings in some concepts and results that have been defined in the literature. Finally, the author studies two inequalities involving the expected value of a fuzzy random variable: the Brunn-Minkowski inequality and the Jensen inequality. The author explores different extensions of the former, and gives an analog for the latter. Potential applications of the authors' results are to the analysis of fuzzy random variables and to statistics with inexact data.<>