Constructive definitions of fuzzy random variables

Miguel López-Diaz and Maria Angeles Gil

Statistics & Probability Letters, 1997, vol. 36, issue 2, 135-143

Abstract: When we deal with a random experiment, we are often interested in functions of the experimental outcomes rather than the outcomes themselves. Fuzzy random variables formalize fuzzy-valued functions of the outcomes in a random experiment, that is, existing imprecise quantification processes. The concepts of fuzzy random variable and its fuzzy expected value, have been introduced by Puri and Ralescu by means of descriptive definitions. Nevertheless, constructive definitions of fuzzy random variables would play an essential role in the constructive definition of their integrals, which will be especially valuable to perform practical computations and to develop further results concerning the integration of these variables. In this paper we present constructive definitions of fuzzy random variables and integrably bounded fuzzy random variables based on the Hausdorff convergence. The use of the last definition to obtain a constructive definition of the fuzzy expected value of an integrably bounded fuzzy random variable is finally discussed.

Keywords: Random; compact; convex; set; fuzzy; random; variable; integrably; bounded; fuzzy; random; variable; [alpha]-level; function; Hausdorff; metric; Hausdorff; convergence (search for similar items in EconPapers)
Date: 1997
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Citations: View citations in EconPapers (7)

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