Using the Degree r∈[0,1] in Defining Rough Fuzzy Sets

Abstract

This paper introduced a new definition of rough fuzzy sets based on a fuzzy ideal l defined on a fuzzy approximation space X,R. This definition considered the degree r∈0,1 in defining the after sets and the before sets of the arbitrary fuzzy relation R on the finite set of objects X. It is shown that this new type of roughness is a generalization to many of previous definitions in the fuzzy case and also in the ordinary case. As an application, it is given a rough fuzzy-connected set notion depending on some degree r∈0,1.