Managing Multiple Fuzzy Information from Statistical Viewpoint and its Engineering Applications

Abstract

In the area of fuzzy theory, one of the important themes is how to extend Dempster-Shafer (D-S) theory to include the process of fuzzy events. In this paper, instead of extending D-S rules, we propose a direction of arguing that elements in a fuzzy domain are all singletons based on the statistical viewpoint and are independent of each other. Therefore, the D-S combination rule can consequently be applied as regularly as in non-fuzzy cases. We first examine the characteristics of how membership functions are defined, which leads to the conclusion that every element in a fuzzy domain is independent, mutually exclusive of each other and consequently is a singleton. We then discuss the relationships between the grades of a membership function and its corresponding statistical probability, and between the probability of a fuzzy event and the probability of every element in its associated data domain. The equations are then derived to calculate the probability of every element in a fuzzy event data domain when both the probability of the event and its membership functions are known. An example is finally given to illustrate how our proposed approach is applied to engineering values.