TRIPOLAR FUZZY SOFT IDEALS AND TRIPOLAR FUZZY SOFT INTERIOR IDEALS OVER Γ−SEMIRING

In this paper, we have introduced the notion of tripolar fuzzy soft $\Gamma -$subsemi-ring,tripolar fuzzy soft ideal, tripolar fuzzy soft interior ideals over $\Gamma -$semiring and also studiedsome of their algebraic properties and the relations between them

Homomorphism in bipolar q—fuzzy soft γ—Semiring

In this paper, we discuss bipolar Q−fuzzy soft Γ−Semiring concept and bipolar Q−fuzzy soft Γ−Semiring homomorphism. Indeed, properties and theorems related to these notions are stated and proved.Publisher's Versio

Characterizations of hemirings by their hh-ideals

In this paper we characterize hemirings in which all $h$-ideals or all fuzzy $h$-ideals are idempotent. It is proved, among other results, that every $h$-ideal of a hemiring $R$ is idempotent if and only if the lattice of fuzzy $h$-ideals of $R$ is distributive under the sum and $h$-intrinsic product of fuzzy $h$-ideals or, equivalently, if and only if each fuzzy $h$-ideal of $R$ is intersection of those prime fuzzy $h$-ideals of $R$ which contain it. We also define two types of prime fuzzy $h$-ideals of $R$ and prove that, a non-constant $h$-ideal of $R$ is prime in the second sense if and only if each of its proper level set is a prime $h$-ideal of $R$

Fuzzy hh-ideals of hemirings

A characterization of an $h$-hemiregular hemiring in terms of a fuzzy $h$-ideal is provided. Some properties of prime fuzzy $h$-ideals of $h$-hemiregular hemirings are investigated. It is proved that a fuzzy subset $\zeta$ of a hemiring $S$ is a prime fuzzy left (right) $h$-ideal of $S$ if and only if $\zeta$ is two-valued, $\zeta(0) = 1$, and the set of all $x$ in $S$ such that $\zeta(x) = 1$ is a prime (left) right $h$-ideal of $S$. Finally, the similar properties for maximal fuzzy left (right) $h$-ideals of hemirings are considered

Some Properties of Q-Neutrosophic Ideals of Semirings

The intention of this paper is to introduce and study some properties of the ideals of semirings using the concept of Q-neutrosophic set

Single valued neutrosophic (M; n)-ideals of ordered Semirings

The aim of this paper is to combine the innovative concept of single valued neutrosophic sets and ordered semirings. It studies ordered semirings by the properties of their single valued neutrosphic subsets. In this regard, we define single valued neutrosophic (m; n)-ideals (SVN-(m; n)-ideals) of ordered semirings. First, we illustrate our new definition by non-trivial examples. Second, we study these SVN-(m; n)-ideals under different operations of SVNS. Finally, we find a relationship between the (m; n)-ideals of ordered semirings and level sets by finding a necessary and sufficient condition for an SVNS of an ordered semiring R to be an SVN-(m; n)-ideal of R

CROSS PRODUCT OF IDEAL FUZZY SEMIRING

If one of the axioms in the ring, namely the inverse axiom in the addition operation, is omitted, it will produce another algebraic structure, namely a semiring. Analogous to a ring, there are zero elements, ideal (left/right) in a semiring, and the cross product of the semiring ideal. The analog of the fuzzy semiring has zero elements, ideal (left/right), and the cross product of the semiring fuzzy ideal associated with the membership value. This paper will discuss the cross-product of two (more) fuzzy ideals from a semiring. Furthermore, the cross-product of two (more) fuzzy ideals from a semiring will always be a semiring fuzzy ideal. But the converse is not necessarily true

Characterization of Gamma Hemirings by Generalized Fuzzy Gamma Ideals

This paper has explored theoretical methods of evaluation in the identification of the boundedness of the generalized fuzzy gamma ideals. A functional approach was used to undertake a characterization of this structure leading to a determination of some interesting gamma hemirings theoretic properties of the generated structures. Gamma hemirings are the generalization of the classical agebraic structure of hemirings. Our aim is to extend this idea and, to introduce the concept of generalized fuzzy gamma ideals, generalized fuzzy prime (semiprime) gamma ideals, generalized fuzzy h -gamma ideals and generalized fuzzy k - gamma ideals of gamma hemirings and related properties are investigated. We have shown that intersection of any family of generalized fuzzy (left, right) h - gamma ideals (k-gamma ideals) of a hemiring is a generalized fuzzy (left, right) h -gamma ideal (k-gamma ideal) of H. Similarly we proved that the intersection of any family of generalized fuzzy prime (resp. semiprime) gamma ideals of H is a generalized fuzzy prime (resp. semiprime) gamma ideal of H. We have proved that a fuzzy subset μ of H is fuzzy h -gamma ideal (k-gamma ideal) if and only if μ is a generalized fuzzy h -gamma ideal (k-gamma ideal) of H. Further level cuts provide a useful linkage betwean the classical set theorey and the fuzzy set theorey. Here we use this linkage to investigate some useful aspects of gamma hemirings and characterize the gamma hemmirings through level cuts in terms of generalized fuzzy (left, right, prime, semiprime) gamma ideals of gamma hemirings. We have also used the concept of support of a fuzzy set in order to obtain some interesting results of gamma hemirings using the generalized fuzzy (left, right, prime, semiprime) gamma ideals of hemirings

2-Absorbing Vague Weakly Complete Γ-Ideals in Γ-Rings

The aim of this study is to provide a generalization of prime vague Γ-ideals in Γ-rings by introducing non-symmetric 2-absorbing vague weakly complete Γ-ideals of commutative Γ-rings. A novel algebraic structure of a primary vague Γ-ideal of a commutative Γ-ring is presented by 2-absorbing weakly complete primary ideal theory. The approach of non-symmetric 2-absorbing K-vague Γ-ideals of Γ-rings are examined and the relation between a level subset of 2-absorbing vague weakly complete Γ-ideals and 2-absorbing Γ-ideals is given. The image and inverse image of a 2-absorbing vague weakly complete Γ-ideal of a Γ-ring and 2-absorbing K-vague Γ-ideal of a Γ-ring are studied and a 1-1 inclusion-preserving correspondence theorem is given. A vague quotient Γ-ring of R induced by a 2-absorbing vague weakly complete Γ-ideal of a 2-absorbing Γ-ring is characterized, and a diagram is obtained that shows the relationship between these concepts with a 2-absorbing Γ-ideal