In the present paper, we introduce the notion of fuzzy Aideals of MV -modules over PMV -algebras and several properties of fuzzy A-ideals are given. Using this concept, a prime fuzzy A-ideal is defined. Using a level set of a fuzzy set in MV -modules, we give a characterization of prime fuzzy A-ideals in MV -modules. Finally, we prove that the homomorphic image and preimage of prime fuzzy A-ide...

This  paper extends the notion of fuzzy $BCK$-subalgebras to fuzzy hyper $BCK$-subalgebras and defines an extended fuzzy $BCK$-subalgebras. This study  considers  a type of fuzzy hyper  $BCK$-ideals  in this  hyperstructure  and  describes   the  relationship  between hyper  $BCK$-ideals and  fuzzy hyper  $BCK$-ideals.  In fact, it tries to introduce   a  strongly  regular  relation  on hyper $...

By means of a kind of new idea, we redefine some kinds of fuzzy ideals in a ring and investigate some of their related properties. The concepts of strong prime (semiprime) generalized fuzzy (bi-, quasi-) ideals in rings are introduced. In particular, we discuss the relationships between strong prime (resp., semiprime) generalized fuzzy (bi-, quasi-) ideals and prime (resp. semiprime) generalize...

Characterizations of fuzzy ideals of a pseudo-BCH-algebra are established. Conditions for a fuzzy set to be a fuzzy ideal are given. The homomorphic properties of fuzzy ideals are provided. Finally, characterizations of Noetherian pseudo-BCH-algebras and Artinian pseudoBCH-algebras via fuzzy ideals are obtained. Mathematics Subject Classi…cation: 03G25, 06F35.

Let $R$ be a commutative ring with identity and $N(R)$ and
 $J\left(R\right)$ denote the nilradical Jacobson radical
 of $R$, respectively. A proper ideal $I$ is called an
 n-ideal if for every $a,b\in R$, whenever $ab\in I$\ $a\notin
 N(R)$, then $b\in I$. In this paper, we introduce study
 J-ideals as new generalization n-ideals in rings.
 $I$\ $R$\ J-ideal $ab\i...

Our aim in this paper is to introduce and study a new sort of fuzzy sublattice (ideal, filter) of a lattice called ) q , ( ∨ ∈ ∈ -fuzzy sublattice (ideal, filter). These fuzzy sublattices (ideals, filters) are characterized by their level sublattices (ideals, filters). Finally, we give a generalization of ) q , ( ∨ ∈ ∈ -fuzzy sublattices (ideals, filters).

In this paper the notion of fuzzy ideals of a Γ-near-ring with respect to a t-norm is introduced and investigated some related properties. This concept of T -fuzzy ideals of a Γ-near-ring is a generalization of the concept of T -fuzzy ideals in near-rings. Also the notions of T -fuzzy ideals of a Γ-near-ring, quotient Γ-near-ring with respect to a t-norm and the sum of T -fuzzy ideals of a Γ-ne...

*Correspondence: [email protected] School of Mathematics Science, Liaocheng University, Liaocheng, Shandong 252059, China Abstract In order to generalize the notions of a (∈,∈ ∨q)-fuzzy subring and various (∈,∈ ∨q)-fuzzy ideals of a ring, a (λ,μ)-fuzzy subring and a (λ,μ)-fuzzy ideal of a ring are defined. The concepts of (λ,μ)-fuzzy semiprime, prime, semiprimary and primary ideals are introdu...

The notions of intuitionistic fuzzy h-ideal and normal intuitionistic fuzzy h-ideal in Γ-hemiring are introduced and some of the basic properties of these ideals are investigated. Cartesian product of intuitionistic fuzzy h-ideals is also defined. Finally a characterization of intuitionistic fuzzy h-ideals in terms of fuzzy relations is obtained. Keywords—Γ-hemiring, fuzzy h-ideal, normal, cart...