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...

In this paper we define a correspondence between the set of all fuzzy hideals of a Γ-hemiring S and the set of all fuzzy h-ideals of the operator hemirings of that Γ-hemiring. We deduce that the lattice of all fuzzy hideals of a Γ-hemiring is isomorphic to the lattice of all fuzzy h-ideals of the operator hemirings of that Γ-hemiring. Finally, the cartesian product of corresponding fuzzy h-idea...

The concept of fuzzy set, which was published by Zadeh in his classic paper [24] of 1965, was applied by many researchers to generalize some of the basic concepts of algebra. The fuzzy algebraic structures play a central role in mathematics with wide applications in many other branches such as theoretical physics, computer sciences, control engineering, information sciences, coding theory, topo...

In this paper, we characterize ordered semigroups in terms of fuzzy quasi-ideals. We characterize left simple, right simple and completely regular ordered semigroups in terms of fuzzy quasi-ideals. We define semiprime fuzzy quasi-ideal of ordered semigroups and characterize completely regular ordered semigroup in terms of semiprime fuzzy quasi-ideals. We also study the decomposition of left and...

In this paper the concept of anti fuzzy ideals of a Γsemigroup has been introduced and some important characterizations have been obtained. Among other results a regular Γ-semigroup has been characterized in terms of anti fuzzy ideals. Finally we show that the set of all the anti fuzzy ideals of a Γ-semigroup forms a semilattice. 2010 AMS Classification: 20M99, 08A72, 20M12

In this paper, the concepts of intuitionistic fuzzy translation to intuitionistic fuzzy Hideals in BCK/BCI-algebras are introduced. The notion of intuitionistic fuzzy extensions and intuitionistic fuzzy multiplications of intuitionistic fuzzy H-ideals with several related properties are investigated. Also the relationships between intuitionistic fuzzy translations, intuitionistic fuzzy extensio...

generalization of Rosenfeld's fuzzy subgroup, and Bhakat and Das's fuzzy subgroup is given in [20]. Lie algebras are so-named in honor of Sophus Lie, a Norwegian mathematician who pioneered the study of these mathematical objects. Lie's discovery was tied to his investigation of continuous transformation groups and symmetries. The structure of the laws in physics is largely based on symmetries....

The notion of intuitionistic fuzzy ideals with thresholds of an ordered semigroup is considered and some of its properties are given. An embedding theorem of the set of all intuitionistic fuzzy ideals with thresholds is presented and the homomorphic images and inverse images of intuitionistic fuzzy ideals with thresholds are studied too. 2010 Mathematics Subject Classification: 06F05

In this paper we investigated some operations on fuzzy h-ideals. Among all the results, we show that the set of all fuzzy left h-ideals of a Γ−hemiring S is zerosumfree hemiring having infinite element 1 under the operations of sum and composition of fuzzy left h-ideals of S. Mathematics Subject Classification: 08A72,16Y99

In this paper, the concept of (∈γ ,∈γ ∨qδ)-fuzzy soft hinterior ideals over a hemiring is introduced and investigated. Some characterization theorems of h-semisimple hemirings are derived in terms of (∈γ ,∈γ ∨qδ)-fuzzy soft left (right) h-ideals and (∈γ ,∈γ ∨qδ)-fuzzy soft hinterior ideals. 2010 AMS Classification: 20M12, 08A72