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Measurability criteria for fuzzy random vectors

Research paper by Xueqin Feng, Yian-Kui Liu

Indexed on: 01 Jul '06Published on: 01 Jul '06Published in: Fuzzy Optimization and Decision Making



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.