Generalization of rough membership function based on α-coverings of the universe

Abstract

In 1982, Pawlak proposed the concept of rough sets with practical purpose of representing indiscernibility of elements. Even it is easy to analyze, the rough set theory built on a partition induced by equivalence relation may not provide a realistic view of relationships between elements in the real-world application. Here, coverings of, or non-equivalence relations on, the universe can be considered to represent a more realistic model instead of partition in which a generalized model of rough sets was proposed. In this paper, based on α-coverings of the universe, a generalized concept of rough membership functions is proposed and defined into three values, minimum, maximum and average. Their properties are examined.