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

This paper introduced a new definition of rough fuzzy sets based on a fuzzy ideal 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].