On the Set Representation of Fuzzy Random Vectors Obtained as Vague Perception of Random Phenomena

Abstract

In this paper, the author tries to reconstruct fuzzy random vector(FRVCs) by using set representation approach. Fuzzy random vectors as vague perception of random phenomena is proposed by author, which have intrinsically both properties of fuzziness and randomness and they are obtained as fuzzy perceptions of ordinary non-fuzzy random vectors. First, FRVCs are re-defined by using the set representation of fuzzy sets. Secondly, adopting the multi-valued logic, the expectation of FRVCs are defined. Finally, some of the statistical properties of FRVCs are studied theoretically.