On the variance of fuzzy random variables

Abstract This paper deals with an expectation and a real-valued variance of fuzzy random variables. The expectation and the variance of a fuzzy random variable is characterized by Frechet's principle in a metric space. We study properties of the variance of a fuzzy random variable and compare it with the common variance of real-valued random variables. Using the expectation and the variance of fuzzy random variables, we consider a linear regression problem and limit theorems.

[1]  R. Kruse,et al.  Statistics with vague data , 1987 .

[2]  Z. Artstein,et al.  A Strong Law of Large Numbers for Random Compact Sets , 1975 .

[3]  R. Schneider.  Convex Bodies: The Brunn–Minkowski Theory: Minkowski addition , 1993 .

[4]  P. Kloeden,et al.  Metric spaces of fuzzy sets , 1990 .

[5]  N. N. Lyashenko,et al.  Limit theorems for sums of independent, compact, random subsets of euclidean space , 1982 .

[6]  R. A. Vitale.  An alternate formulation of mean value for random geometric figures * , 1988 .

[7]  W. Nather.  Linear statistical inference for fuzzy data , 1995, Proceedings of 3rd International Symposium on Uncertainty Modeling and Analysis and Annual Conference of the North American Fuzzy Information Processing Society.