2015 Volume 2015 Pages 118-123
In this paper, the author numerically investigates the convergence properties of estimators concerned with expectations for a class of fuzzy random sets, where the fuzzy random set is considered as a model of the capricious vague perception of a crisp phenomenon or a crisp random phenomenon. First, fuzzy random sets as vague perceptions of crisp phenomena and their extended one as vague perceptions of random phenomena are reviewed. Secondly applying the standard strong law of large numbers(SLLN) for the random elements in a separable Banach space, the convergence property of estimators for expectations of random fuzzy sets is examined, and finally they are confirmed numerically by simulation studies. The proposed fuzzy random sets are expected to apply to the social system modelings including the mathematical finance, where many data have both the properties of vagueness and randomness.
