(ϑ, T)-fuzzy rough approximation operators and the TL-fuzzy rough ideals on a ring

In this paper, we consider a ring as a universal set and study (ϑ, T)-fuzzy rough approximation operators with respect to a TL-fuzzy ideal of a ring. First, some new properties of generalized (ϑ, T)-fuzzy rough approximation operators are obtained. Then, a new fuzzy algebraic structure – TL-fuzzy rough ideal is defined and its properties investigated. And finally, the homomorphism of (ϑ, T)-fuzzy rough approximation operators is studied.