On the Set Operational Laws in Uncertain Sets Using Inverse Membership Functions

Abstract

It would be useful to construct uncertain sets using set operations applied on other uncertain sets. When the membership functions of the components are known, finding the membership function of the produced uncertain set is straightforward. However, when only the inverse membership functions of components are available, one must first find the membership functions and then use the known relations. Here, we establish the relation between the inverse membership function of the produced uncertain set and its component’s inverse membership functions. Some simple examples verify the findings. We also denote how it can be used to easily calculate expected value of such an uncertain set just by using the inverse membership functions of its components.