Radon-Nikodym Theorem for Fuzzy Set-Valued Measures*

Abstract

We study fuzzy set-valued measures in a Banach space and their relationships with fuzzy random variables. This theory is motivated by the need for a rigorous framework for the problem of inexact measurement. Our main result is a theorem of the Radon-Nikodym type for a fuzzy measure which is absolutely continuous with respect to a probability measure. Our result extends corresponding results for vector measures and for set-valued measures.