Annals of Communications in Mathematics

AbstractIn this paper, we introduce the notion of a fuzzy soft tri-ideal over Γ−semiring. We characterize the regular Γ−semiring in terms of fuzzy soft tri-ideals, and study some of the properties. M is a regular Γ−semiring, E be a parameters set and A ⊆ E. If (µ, A) is a fuzzy soft left tri-ideal over M, then (µ, A) is a fuzzy soft right ideal over M.

AbstractIn this paper we introduce the notion of anti fuzzy ideals, anti fuzzy k−ideals of ordered semirings and we study the properties of anti fuzzy ideals, anti fuzzy k−ideals, homomorphic and anti homomorphic image and pre-image of fuzzy ideals, anti fuzzy ideals and anti fuzzy k−ideals of an ordered semiring. We characterize the ideals of an ordered semiring in terms of anti fuzzy k−ideals.

AbstractIn this paper, we introduce the notion of interval valued fuzzy prime ideals of Γ−semirings.We study, some properties of prime ideals of a Γ−semirng in terms of interval valued fuzzy ideals.

AbstractWe introduce the notion of ideal, prime ideal, filter, fuzzy ideal, fuzzy prime ideal, fuzzy filter of an ordered semiring and study their properties and relations between them. We characterize the prime ideals and filters of an ordered semiring with respect to fuzzy ideals and fuzzy filters respectively. We proved a fuzzy subset µ is a fuzzy filter of an ordered semiring M if and only if µMT β, : X → [0, 1] is a fuzzy filter of an ordered semiring M. M and N be ordered semirings and ϕ : M → N be an onto homomorphism. If f is a ϕ homomorphism invariant fuzzy filter of M then ϕ(f) is a fuzzy filter of N.

Abstractn this section, we introduce the notions of a left and a right translational invariant fuzzy subsets of a Γ−semigroup M, as well as the concept of a unit with respect to a fuzzy subset, and study their properties. We also prove that if μ is a translational invariant fuzzy subset of a commutative Γ−semigroup with unity, then the principal ideal generated by an element and μ that contains a unity element is a prime ideal of the Γ−semigroup.