On a class of fuzzy random vectors obtained as vague perception of random phenomena

The purpose of this paper is to investigate some of the statistical properties of fuzzy random vectors (FRVCs), which have intrinsically both properties of fuzziness and randomness and they are considered to be obtained as vague perceptions of ordinary non-fuzzy random vectors. First, the concept of FRVCs is introduced by using the set representation method of fuzzy sets. Secondly, by applying multi-valued logic (extension principle of fuzzy sets), reasonable definitions of expectations of FRVCs are proposed, and finally some of their statistical properties are studied theoretically