On fuzzy random vectors as vague perceptions of random phenomena and their statistical moments

In this paper, the author proposes a kind of fuzzy random vectors (FRVCs), which are obtained as vague perceptions of random phenomena, and hence have intrinsically both properties of fuzziness and randomness. FRVCs is expected to be a theoretical base for investigating how to extract the valuable information from the data obtained as the vague observation of random phenomena. First, the concept of FRVCs as vague perceptions of random vectors is introduced, where fuzzy set theory is adopted in order to represent the vagueness due to perceptions of random phenomena by persons, as well as probability theory to describe their randomness. Next, by applying the multi-valued logic and the theory of correspondences, the statistical moments of FRVCs up to the second ones are proposed. Finally, some of the properties of the proposed FRVCs and their statistical moments are investigated theoretically