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...

first we show that the cosets of a fuzzy ideal μ in a bck-algebrax form another bck-algebra  x/μ (called the fuzzy quotient bck-algebra of x by μ). also we show thatx/μ is a fuzzy partition of x and we prove several some isomorphism theorems. moreover we prove that if the associated fuzzy similarity relation of a fuzzy partition p of a commutative bck-algebra iscompatible, then p is a fuzzy quo...

The purpose of this paper is to introduce Shi’s (quasi-)uniformity structure in the context of fuzzy soft sets. We define the notion of a fuzzy soft (quasi-)uniformity in the sense of Shi. We give the relations between a fuzzy soft (quasi-)uniformity and a fuzzy soft cotopology. Also, we investigate the relations between fuzzy soft remote neighborhood structures which are generated by a given f...

In this paper, using the idea of quasi-coincidence of a fuzzy point with a fuzzy set, the concept of (∈,∈ ∨q)fuzzy interior ideals in a Γ-semigroup has been introduced and some of their important related properties have been investigated. Characterizations of regular Γsemigroups, intra-regular Γ-semigroups, and semisimple Γ-semigroups in terms of (∈,∈ ∨q)-fuzzy interior ideals have also been ob...

In our recent paper we have established close relationships between state reduction of a fuzzy recognizer and resolution of a particular system of fuzzy relation equations. In that paper we have also studied reductions by means of those solutions which are fuzzy equivalences. In this paper we will see that in some cases better reductions can be obtained using the solutions of this system that a...

A pseudo-addition in BL-algebras is a binary operation that is associative and non commutative. The aim of this paper is to use the notion of pseudo-addition to study the notion of ideal and fuzzy ideal as a natural generalization of that of ideal and fuzzy ideal in MV-algebras. Using a pseudo-addition, we characterize fuzzy ideals and also obtain a concrete description of the fuzzy ideals gene...

The concepts of L-fuzzy ideal generated by a L-fuzzy subset, L-fuzzy prime and completely prime ideal where L is a complete lattice are considered and some results are proved

in this note first we define the notions of fuzzy positive implicativehyper bck-ideals of types 1,2,3 and 4. then we prove some theorems whichcharacterize the above notions according to the level subsets. also we obtainthe relationships among these notions, fuzzy (strong, weak, reflexive) hyperbck-ideals and fuzzy positive implicative hyper bck-ideals of types 5,6,7and 8. then, we define the no...

The aim of this paper is to study L-fuzzy uniformizable spaces. A new kind of topological fuzzy remote neighborhood system is defined and used for investigating the relationship between L-fuzzy co-topology and L-fuzzy (quasi-)uniformity. It is showed that this fuzzy remote neighborhood system is different from that in [23] when U is an Lfuzzy quasi-uniformity and they will be coincident when U ...