A Novel of Ideals and Fuzzy Ideals of Gamma-Semigroups

Abstract

In this paper, we define new types of ideals, fuzzy ideals, almost ideals, and fuzzy almost ideals of Γ -semigroups by using the elements of Γ . We investigate properties of them.

New Types of Intuitionistic Fuzzy Ideals in Г-Semigroups

“…A sub-Γ-semigroup K of a Γ-semigroup E is called a bi-ideal of E if JΓEΓJ ⊆ J. Definition 2.1 [8]. Let E be a Γ-semigroup and J be a nonempty subset of E, for all e ∈ E and α, β ∈ Γ.…”

“…The following conditions define the types of fuzzy almost ideal on semigroups. Definition 2.3 [8]. A fuzzy set ξ of a semigroup J is considered to be:…”

“…The structure of the ideal theory is important in the study of semigroups, and many researchers use the knowledge of ideals in studies related to Gammasemigroups in fuzzy semigroups. For instance, Chinram [3] studied almost quasi-Γ-ideal and fuzzy almost quasi-Γ-ideals in Γ-semigroups; Marapureddy and Doradla [8] studied weak interior ideals of Γ-semigroups; and Majumder and Mandal [3] studied fuzzy generalized bi-ideal in Γ-semigroups. In regards to the concept of intuitionistic fuzzy ideals, several researchers expanded on this idea [4][5][6][7].…”

“…In regards to the concept of intuitionistic fuzzy ideals, several researchers expanded on this idea [4][5][6][7]. Recently, in 2021, Simuen et al [8], Simuen et al studied the concept of ideals and fuzzy ideals of Γ-semigroups.…”

On inf -Hesitant Fuzzy Γ -Ideals of Γ -Semigroups

“…Many classical notions and results of (ternary) semigroups have been extended and generalized to Γ-semigroups, by many mathematicians, for instance, Siripitukdet and Iampan [18,19], Siripitukdet and Julatha [20], Dutta and Adhikari [21,22], Saha and Sen [23][24][25], Hila [26,27], and Chinram [28,29]. Simuen, Iampan, Chinram, Sardar, Majumder, Dutta, and Davvaz [30][31][32][33][34][35] studied theory of Γ-semigroups via fuzzy subsets. Uckun et al [36] studied theory of Γ-semigroup via intuitionistic fuzzy subsets.…”