Abstract
In this paper, the author investigates the convergent properties of estimators concerned with expectations for a class of vague random phenomena, 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 random perceptions of non-random or random phenomena are investigated, and their expectations are also considered. Secondly applying the standard Strong Law of Large Numbers(SLLN) for the random elements in a separable Banach space, the convergent properties of estimators for expectations of the proposed fuzzy random sets are examined, and finally they are confirmed numerically by simulation studies.
