Abstract
In this paper, the author will investigate fuzzy martingales for a class of fuzzy random vectors(FRVCs for short), where FRVCs are the improved ones of the previously proposed by the author[1] and partly investigated[2] 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, their expectations and conditional expectations are reviewed, where the set representation approach of fuzzy sets and theory of random correspondences are applied for deriving their reasonable definitions. Secondly, the reasonable definition of fuzzy martingales for the sequence of the proposed FRVCs is derived, and some preliminary results are studied theoretically.
