On Variances for a Class of Fuzzy Random Vectors

Abstract

In this paper, the author will investigate variances for a class of fuzzy random vectors(FRVCs for short), where FRVCs are the improved ones of the previously proposed by the author[I] and partly investigated[2, 3] as the vague perception of crisp random phenomena. The FRVCs proposed here have intrinsically both properties of fuzziness and randomness and they are considered to be obtained as fuzzy perceptions of ordinary non-fuzzy random vectors.

First, the proposed FRVCs and their expectations are reviewed, where the set representation approach of fuzzy sets with the help of the multivalued logic are applied for deriving their reasonable definitions. Secondly, the variances of FRVCs are derived from both viewpoints of multvalued-logic approach and the Frëchet approach, and some preliminary results are studied theoretically.