Fuzzy Gamma Semimodules over Gamma Semirings

Arxiv preprint arXiv:1101.4720, 2011

The purpose of this paper is to investigate some properties of fuzzy ideals and fuzzy bi-ideals in Γ-semigroups and to introduce the notion of fuzzy quasi ideals in Γ-semigroups. Here we also characterize a regular Γ-semigroup in terms of fuzzy quasi ideals.

Hikari publication, 2011

In this paper, the notion of an anti fuzzy bi-Γ-ideals in Γ-semigroups is introduced, and investigated some of their related properties. Further complete and normal anti fuzzy ideals in Γ-semigroups are investigated.

Earthline Journal of Mathematical Sciences, 2019

Let M be a Γ-semiring. In this paper we obtain some properties of L-fuzzy ideals in M x M. Our results take inspiration from [M. Murali Krishna Rao and B. Vekateswarlu, L-fuzzy ideals in Γ-semiring, Annals of Fuzzy Mathematics and Informatics 10(1) (2015), 1-16]. The readers are left with a conjecture.

Advances in Fuzzy Systems, 2018

We apply the hesitant fuzzy sets theory to Γ-semigroups and provide some characterizations of hesitant fuzzy left (right and bi-) ideals. We introduce the hesitant fuzzy left (resp., right and two-sided) ideal, hesitant fuzzy bi-ideal, and hesitant fuzzy interior ideal in Γ-semigroup and study some properties of them. Finally, a characterization of a simple Γ-semigroup by means of a hesitant fuzzy simple Γ-semigroup is obtained.

In this paper, we characterize the relationship between fuzzy ideals, fuzzy interior ideals, fuzzy bi-ideals and the characteristic function of fuzzy ideals in PO-Γ-semigroups. Also we proved the equivalent statements, necessary and sufficient conditions on partial ordered Γsemigroups.

The notions of bipolar valued fuzzy subsemigroup, bipolar valued fuzzy bi-ideal, bipolar valued fuzzy (1,2)-ideal and bipolar valued fuzzy ideal in a Γ-semigroup are introduced. Some characterizations are also obtained.

The Korean Journal of Mathematics, 2020

In this article, we initially present the concept of the fuzzy generalized m-bi-ideals in semigroups, then making use of their important types like prime, semiprime and strongly fuzzy generalized m-bi-ideals, we give the important characterizations of the semigroups. We also characterize the m-regular and m-intraregular semigroups using the properties of the irreducible and strongly irre-ducible fuzyy generalized m-bi-ideals.

Malaysian Journal of Fundamental and Applied Sciences

The advancement in the fascinating area of fuzzy set theory has become area of much interest, generalization of the existing fuzzy subsystems of other algebraic structures is very important to tackle more current real life problems. In this paper, we give more generalized form of regular ordered gamma semigroups in terms of (E,EVq_k)-fuzzy gamma ideals. Particularly, we characterized left regular, right regular, simple and completely regular ordered gamma semigroups in terms of this new notion. Some necessary and sufficient conditions for ordered gamma semigroup to be completely regular are provided in this paper.

IAEME PUBLICATION, 2020

In this paper, the terms Fuzzy regular Γ-Subsemigroup, λ-Cut, Fuzzy left and right regular Γ-Subsemigroup, Fuzzy intra regular Γ-Subsemigroup, Fuzzy completely Regular Γ-subsemigroup, ideal generated by the ordered fuzzy point 𝒂𝜆, fuzzy semi simple in a PO Gamma semigroup are introduced. It is proved that (1) If f is fuzzy regular Γ-subsemigroup of S then f is fuzzy Idempotent,(2) If f is fuzzy completely regular then f is regular, left regular and right regular, (3) If 𝒂𝜆 is fuzzy regular then 𝒂𝜆 is fuzzy semi simple, (4) If an orderd fuzzy point 𝒂𝜆 of S is left(right) regular Γsemigroup then 𝒂𝜆 is fuzzy semi simple, (5) If 𝒂𝜆 is fuzzy intra regular Gamma semigroup then 𝒂𝜆 is fuzzy semi simple

Arxiv preprint arXiv:1101.3081, 2011

In this paper some fundamental relationships of a Γ-semigroup and its operator semigroups in terms of intuitionistic fuzzy subsets, intuitionistic fuzzy ideals, intuitionistic fuzzy prime(semiprime) ideals, intuitionistic fuzzy ideal extensions are obtained. These are then used to obtain some important characterization theorems of Γ-semigroups in terms of intuitionistic fuzzy subsets so as to highlight the role of operator semigroups in the study of Γ-semigroups in terms of intuitionistic fuzzy subsets.

Journal of Mathematics and Computer Science , 2020

In this article, we present the idea of the fuzzy m-bi-ideals in semi-groups and describe their basic algebraic properties. We also develop the forms of the fuzzy m-bi-ideals generated by an element, a subset, and a sub-semi-group of the semi-group. Important characterizations of semi-groups and their different types like m-regular semi-groups and m-intraregular semi-groups have been given through demonstrating examples and using properties of fuzzy m-bi-ideals in semi-groups.

academicjournals.org

We generalize the Davvaz's paper to the fuzzy submodules of gamma modules and give some characterizations of fuzzy gamma modules.

2013

Generalizing the notions of -fuzzy left (right) ideal, -fuzzy quasi-ideal, and -fuzzy bi-ideal, the notions of -fuzzy left (right) ideal, -fuzzy quasi-ideal and -fuzzy bi-ideal of semigroups are defined. Regular, intra regular and semisimple semigroups are characterized by the properties of these fuzzy ideals.

Applied Mathematics & Information Sciences, 2014

The aim of this paper is to apply the concept of fuzzy soft sets over a Γ -semigroup. Here the notion of fuzzy soft ideals over a Γ -semigroup has been introduced. The special union, intersection and product of fuzzy soft ideals over a Γ -semigroup have been defined and proved that these are also fuzzy soft Γ -ideals over the Γ -semigroup.

In this paper the notion of fuzzy prime ideal in Γ-semigroups has been introduced and studied. Relationship between prime ideals of a Γ-semigroup and that of its operator semigroups have been obtained which are used to revisit analogous results on ideals of Γ-semigroups and its operator semigroups.