Intuitionistic fuzzy rough sets are investigated in a general framework which includes generalizations of many related results in early literatures. A new definition of intuitionistic fuzzy rough sets is given with the analysis of its basic properties based on the notion of two universes, general binary relations, and a pair ðT , IÞ of intuitionistic fuzzy t-norm T and intuitionistic fuzzy impl...

Recently, the rough set and fuzzy set theory have generated a great deal of interest among more and more researchers. Granular computing (GrC) is an emerging computing paradigm of information processing and an approach for knowledge representation and data mining. The purpose of granular computing is to seek for an approximation scheme which can effectively solve a complex problem at a certain ...

Abstract. In this paper, we introduce the concept of T−fuzzy interior ideal, T−fuzzy simple, T−fuzzy bi-ideal, and generalized T−fuzzy bi-ideal of a Γ−semigroup. We characterize Γ−semigroups through T−fuzzification. We find equivalent conditions on these fuzzy subsets in simple Γ−semigroups and Γ−semigroups. Finally, we establish a necessary and sufficient condition for a T -fuzzy bi-ideal to b...

Multi–granulation is an improvement of the classical rough set theory since it uses a family of binary relations instead of of a single indiscernibility relation for the constructing of approximation. In this paper, the multi–granulation rough set approach is further generalized into fuzzy environment. A family of fuzzy T–similarity relations are used to define the optimistic and pessimistic fu...

We inquire further into the properties on fuzzy closed ideals. We give a characterization of a fuzzy closed ideal using its level set, and establish some conditions for a fuzzy set to be a fuzzy closed ideal. We describe the fuzzy closed ideal generated by a fuzzy set, and give a characterization of a finite-valued fuzzy closed ideal. Using a t-norm T , we introduce the notion of (imaginable) T...

Data used in machine learning applications is prone to contain both vague and incomplete information. Many authors have proposed to use fuzzy rough set theory in the development of new techniques tackling these characteristics. Fuzzy sets deal with vague data, while rough sets allow to model incomplete information. As such, the hybrid setting of the two paradigms is an ideal candidate tool to c...

In this paper, we introduce the notion of fuzzy ideal,fuzzy weak ideal,fuzzy weakly prime left ideal and fuzzy prime left ideal system of a near-subtraction semigroup. We characterize fuzzy weak ideal and fuzzy ideal of a near-subtraction semigroup X through weak ideal and ideal of X respectively. We have shown that a fuzzy left ideal μ of a nearsubtraction semigroup X is a fuzzy weakly prime l...