On Second Statistical Moments for Capricious Vague Perceptions

Abstract

In this paper, the author investigates the statistical moments such as expectations and variances 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, the class of fuzzy random sets, which has been proposed by author [1][2][3], where the vague perception of a crisp phenomenon fluctuates slightly but randomly by the state of a capricious person'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 vague perceptions of crisp random phenomena, and their expectations and variances are investigated from the viewpoint of the multi-valued logic.

On Asymptotic Distributions of Estimators Concerned with Fuzzy Random Data as Vague Perceptions of Crisp Random

“…The class of fuzzy sets adopted in this paper is inspired by Kwakernaak[6], Kruse and Meyer [7], Kruse, Gebhardt and Klawonn [8], and the revised one previously proposed by the author(see e.g., [9,10,11,12]. )…”

“…is a collection of realized fuzzy sets given by (10), and 1 A i j (ω) is a characteristic function defined by (9).…”

On Two-Dimensional Fuzzy Random Data as Vague Perceptions of Crisp Phenomena

“…In recent years, motivated by the importance for treating the data exhibiting both vagueness and randomness, fuzzy random variables or more generally fuzzy random sets have been intensively investigated by many researchers with various definitions [1,2,3,4,5,6,7,8,9,10].…”