On Second Statistical Moments for Capricious Vague Perceptions

Abstract

In this paper, the author investigates the statistical moments such as expectations and variancesfor a class of fuzzy random sets, where the fuzzy random set is considered as a model of the capriciousvague perception of a crisp phenomenon or a crisp random phenomenon.First, the class of fuzzy random sets, which has been proposed by author[1–3], where the vagueperception of a crisp phenomenon fluctuates slightly but randomly by the state of a capriciousperson’s mind, is refined and its expectation and variance are introduced.Secondly, the refined class of fuzzy random sets is extended to the models for the capricious vagueperceptions of crisp random phenomena, and their expectations and variances are investigated fromthe viewpoint of the multi-valued logic.