Measurability criteria for fuzzy random vectors

Authors:
Xueqin Feng;Yian-Kui Liu
Affiliations:
College of Economics, Hebei University, Baoding, China 071002;College of Mathematics and Computer Science, Hebei University, Baoding, China 071002
Venue:
Fuzzy Optimization and Decision Making
Year:
2006

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Abstract

Fuzzy random vector is a measurable map from a probability space to a collection of fuzzy vectors. Our aim in this paper is to discuss the measurability criteria for fuzzy random vectors, and show that under mild assumption, the measurability criteria for upper semicontinuous fuzzy random vectors can be expressed in several different but equivalent formulations. Finally, applying the obtained results, we resolve an open problem about the relationship between fuzzy random vectors and fuzzy random variables.