On The Generalization of Fuzzy Rough Approximation Based on Asymmetric Relation

Abstract

An asymmetric relation, called a weak similarity relation, is introduced as a more realistic relation in representing the relationship between two elements of data in a real-world application. A conditional probability relation is considered as a concrete example of the weak similarity relation by which a covering of the universe is provided as a generalization of a disjoint partition. A generalized concept of rough approximations regarded as a kind of fuzzy rough set is proposed and defined based on the covering of the universe. Additionally, a more generalized fuzzy rough approximation of a given fuzzy set is proposed and discussed as an alternative to provide interval-valued fuzzy sets. Their properties are examined.