Perception-Based Estimations of Fuzzy Random Variables: Linearity and convexity

A set of perceived random events is given by a fuzzy random variable, and an estimation of real random variables is represented by a functional on real random variables. The perception-based extension of estimation regarding random events is introduced, extending the functional to a functional of fuzzy random variables. This paper discusses some conditions and various properties of the extended estimations, for example, monotonicity, continuity, linearity, sub-additivity/super-additivity, convexity/concavity. Several examples of the perception-based extended estimations are investigated. This paper analyzes the general cases, where the estimations do not have monotone properties, from the viewpoint of convexity/concavity. The results can be applicable to other estimations in engineering, economics and so on.