On Two-Dimensional Fuzzy Random Data with Polygon-form Level Sets as Vague Perception of Crisp Random Phenomena

Abstract

In this paper, the author investigates numerically a class of two-dimensional fuzzy random sets(abbreviated as FRSs), which is one case of those proposed by the author[1] as models of vague capricious perceptions of crisp random phenomena.

First, the basic results concerned with two-dimensional FRSs as vague capricious perceptions of random phenomena are reviewed. Expectations of two-dimensional FRSs, their estimators, and distances between expectations and their estimators are also reviewed briefly.

Finally, estimates for expectations of two-dimensional FRSs and their estimation errors are numerically examined by simulation studies, when their level sets are given by polygon-form ones at every level.