On Expectations and Conditional Expectations for a Class of Fuzzy Random Vectors

抄録

In this paper, the author proposes a class of fuzzy random vectors(FRVCs for short), which is the improved one of the previously proposed by the author[1] 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 improved FRVCs are introduced by using the set representation approach of fuzzy sets and some their properties are investigated. Secondly, applying the multi-valued logic, the expectations of FRVCs are proposed and some their basic properties are investigated. Finally, the reasonable definition of conditional expectations for the proposed FRVCs is studied theoretically.