In the present paper, the notions of interval valued (∈,∈ ∨(k̃∗, qk̃))-fuzzy bi-ideals and interval valued (∈,∈ ∨(k̃∗, qk̃))-fuzzy quasiideals of ordered semigroups are introduced, and their related properties are investigated. Furthermore, we characterize different classes of ordered semigroups by using the properties of these interval valued generalized fuzzy ideals. 2010 AMS Classification: 06F0...

Our aim in this paper is to introduce and study a new sort of fuzzy ternary subsemigroup (left ideal, right ideal, lateral ideal, quasi-ideal, bi-ideal) of a ternary semigroup, called interval-valued (α,β )-fuzzy ternary subsemigroup (left ideal, right ideal, lateral ideal, quasi-ideal, bi-ideal). We also characterize regular ternary semigroups in terms of these interval-valued fuzzy ideals.

In this paper, we attempt to investigate the connection between various types of ideals (for examples $(m, n)$-ideal, bi-ideal, interior ideal, quasi ideal, prime ideal and maximal ideal) of an ordered semigroup $(S,cdot ,leq)$ and the correspond hyperideals of its EL-hyperstructure $(S,*)$ (if exists). Moreover, we construct the class of EL-$Gamma$-semihypergroup associated to a partially orde...

In this paper basic notions of rough intuitionistic fuzzy set in semigroups are given and we discuss some of its basic properties. We introduce the notions of rough intuitionistic fuzzy left (right, two-sided, bi-, (1, 2)-) ideals in a semigroup and give some properties of such ideals.

let  $r$ be a commutative noetherian ring and $i$ be an ideal of $r$. we say that $i$ satisfies the persistence property if  $mathrm{ass}_r(r/i^k)subseteq mathrm{ass}_r(r/i^{k+1})$ for all positive integers $kgeq 1$, which $mathrm{ass}_r(r/i)$ denotes the set of associated prime ideals of $i$. in this paper, we introduce a class of square-free monomial ideals in the polynomial ring  $r=k[x_1,ld...

We introduce and use the concept of (∈γ ,∈γ ∨qδ)-fuzzy (left, right, bi-) ideals to study the structural properties of a non-associative algebraic ordered structure. We characterize an intra-regular ordered AGgroupoid by these generalized fuzzy ideals. 2010 AMS Classification: 06F05, 20M12, 08A72

In this paper the concept of the extensions of intuitionistic fuzzy ideals in a semigroup has been extended to a Γ-Semigroups. Among other results characterization of prime ideals in a Γ-Semigroups in terms of intuitionistic fuzzy ideal extension has been obtained.

In this study, by generalizing the notion of fuzzy bi-ideals ordered semirings, (∈,∈∨(κ*,qκ))-fuzzy is established. We prove that are but converse not true, and an example provided to support proof. A condition given under which semirings coincide with bi-ideals. An equivalent certain correspondences between presented. Moreover, (κ*,κ)-lower part described depicted in terms several classes semi...