Fuzzy Ideals Research Articles

Applications of Bipolar Fuzzy Almost Ideals in Semigroups

In this paper, we give the concept of bipolar fuzzy almost ideal, minimal almost bipolar fuzzy ideals, and prime (semiprime, strongly prime) bipolar fuzzy almost ideals in semigroups. We investigate the basic properties of bipolar fuzzy almost ideals in semigroups. Finally, we study the relationship between almost ideals and bipolar fuzzy almost ideals in semigroups.

Novel categorical relations between $ \mathcal{L} $-fuzzy co-topologies and $ \mathcal{L} $-fuzzy ideals

The goal of this paper is to construct novel relationships among $ \mathcal{L} $-fuzzy ideal, $ \mathcal{L} $-fuzzy co-topological, and $ \mathcal{L} $-fuzzy pre-proximity spaces in complete residuated lattices. We illustrate and prove four functors between the categories of those spaces and finally, we give examples.

Double fuzzy $ \alpha $-$ \eth $-continuous multifunctions

Double fuzzy $ \alpha $-$ \eth $-continuous multifunctions

Anti-neutrosophic fuzzy ideals of near-rings

Anti-neutrosophic fuzzy ideals of near-rings

Multipolar neutrosophic subalgebras/ideals of UP-algebras

The notion of neutrosophic m-polar fuzzy sets is much wider than the notion of m-polar fuzzy sets. In this paper, we apply the theory of neutrosophic m-polar fuzzy set on UP-algebras. We introduce the concepts of neutrosophic m-polar fuzzy subalgebras, neutrosophic m-polar fuzzy ideals and neutrosophic m-polar fuzzy strong ideals and some essential properties are discussed. We characterize neutrosophic m-polar fuzzy subalgebras in terms of fuzzy subalgebras and subalgebras of UP-algebras.

Anti-Homomorphisms in Bipolar Fuzzy Ideals and Bi-Ideals of Γ-Near Rings

Anti-Homomorphisms in Bipolar Fuzzy Ideals and Bi-Ideals of Γ-Near Rings

On 1-Absorbing Fuzzy Ideals of Commutative Semirings

In this study, the algebraic structure of 1-absorbing ideals is first examined and applied to fuzzy sets, along with an investigation into the relationships and algebraic properties between them. The contribution to this work's literature involves examining 1-absorbing fuzzy primary ideals. Features of 1-absorbing fuzzy primary ideals are explored, and it is demonstrated, for instance, that I is deemed a 1-absorbing fuzzy primary ideal of P if I is a fuzzy primary ideal of P. Additionally, I is considered a 2-absorbing fuzzy primary ideal of P if I is a 1-absorbing fuzzy primary ideal of P. Furthermore, these theorems are elucidated through specific examples.

Some Properties of Fuzzy Ideals of Unit Regular Semigroups

This paper introduces the concept of unit-regular fuzzy ideals of semi groups, which is a generalization of regular fuzzy ideals. Several of their significant related properties have been examined. According to the unit-regular semi group, the fuzzy-interior-ideal, fuzzy-ideal, fuzzy-bi-ideal, and fuzzy-generalized-bi-ideal have all been described.

General types of sup -hesitant fuzzy ideals of ternary semigroups

General types of sup -hesitant fuzzy ideals of ternary semigroups

Spherical interval valued fuzzy ideals which coincide in semigroups

The concept of spherical fuzzy set was introduced by Gun et al. in 2018. It is generalization of Pythagorean fuzzy set. Our main paper, we give the concepts of spherical interval valued fuzzy ideals in semigroups, and properties of a spherical fuzzy ideal in semigroups with prove. Moreover, we investigate necessary and sufficient conditions of coincidences spherical interval valued fuzzy ideals in semigroups.

Ideals of BCK-algebras and BCI-algebras Based on a New Form of Fuzzy Set

Ideals in BCK/BCI algebra based on $Y_J^{\varepsilon}$-fuzzy sets are studied. The fundamental properties of the level set of $Y_J^{\varepsilon}$-fuzzy sets are investigate first. The concept of (closed) $Y_J^{\varepsilon}$-fuzzy ideals in BCK/BCI-algebras is introduces, and several properties are investigated. The relationship between $Y_J^{\varepsilon}$-fuzzy ideal and $Y_J^{\varepsilon}$-fuzzy subalgebra are discussed, and also the relationship between $Y_J^{\varepsilon}$-fuzzy ideal and fuzzy ideal is identified. The characterization of (closed) $Y_J^{\varepsilon}$-fuzzy ideal using the Y-level set is established. The necessary and sufficient conditions for $Y_J^{\varepsilon}$-fuzzy ideal to be closed is explored, and conditions for $Y_J^{\varepsilon}$-fuzzy subalgebra to be $Y_J^{\varepsilon}$-fuzzy ideal are provided.

Multi – Fuzzy Ideals of Г - Near Ring

Multi – fuzzy set theory is an extension of fuzzy set theory. In this paper, we define the multi fuzzy ideals of Г - near ring. Also, the notion of anti multi fuzzy ideals of a Г - near ring is introduced and investigated some related properties. This concept of multi fuzzy ideals of a Г - near ring is a generalization of the concept of fuzzy ideals in Г - near rings. Also, we define the multi-level subsets and multi anti level subsets of a multi fuzzy sub Г - near ring of a Г- near ring. In this paper we define the multi level subset and multi anti level subset of AUB. The purpose of this study establishes the algebra of multi fuzzy Г- near ring.

LATTICE OF A FUZZY PRIME IDEALS IN AN ORDERED SEMIGROUP

This paper introduces the concept of lattices of prime fuzzy ideals, which extends the classical theory of lattices of prime ideals in ring theory to the fuzzy setting. In this paper, we propose some examples and properties related to lattices of prime fuzzy ideals, contributing to the knowledge in fuzzy algebra. Think about an ordered semigroup ℛ. Plotting the function f from ℛ to the closed interval [0,1] defines a fuzzy subset of ℛ, where [0,1] ϵ ℛ. In order to explore prime ideals in rings, semigroups, and ordered semigroups in terms of fuzzy subsets, we build an ordered semigroup ℛ with ordered fuzzy points. To study, we presented the thoughts of ℒ-fuzzy prime ideals of an ordered semigroups ℛ, which forms a completelattice obeying the law relating the operations of multiplication and addition.

INTUITIONISTIC FUZZY ASPECTS OF MULTIPLICATION N-GROUPS

Intuitionistic fuzzy (IF) sets were first put forward by K. Atanassov as a generalised notation for fuzzy sets in 1983. The concepts of intuitionistic fuzzy near rings, intuitionistic fuzzy N-groups, intuitionistic fuzzy N-subgroups, intuitionistic fuzzy ideals of N-group are described by P. Saikia, L. K. Barthakur and H. K. Saikia in [10, 11]. Fuzzy distributive modules are studied by Sh. B. Semeein and I. M. A. Hadi in [4]. Intuitionistic fuzzy multiplication modules are studied by P. K. Sharma in [13]. We extend the notion of intuitionistic fuzzy multiplication modules to intuitionistic fuzzy multiplication N-groups. Here, we define intuitionistic fuzzy multiplication N-group and some basic definitions that are needed in this sequel. The relations ship of multiplication N-groups, intuitionistic fuzzy multiplicationN-groups, DN-groups and intuitionistic fuzzy DN-groups are also studied.

AN INVESTIGATION OF F-CLOSURE OF INTUITIONISTIC FUZZY SUBMODULES OF A MODULE

In this paper, we introduce the notion of F-closure of intuitionistic fuzzy submodules of a module M. Our attempt is to investigate various characteristics of such an F-closure. If F is a non-empty set of intuitionistic fuzzy ideals of a commutative ring R and A is an intuitionistic fuzzy submodule of M, then the F-closure of A is denoted by ClM F (A). If F is weak closed under intersection, then (1) F-closure of A exhibits the submodule character, and (2) the intersection of F-closure of two intuitionistic fuzzy submodules equals the F-closure of intersection of the intuitionistic fuzzy submodules. If F is weak closed under intersection, then the submodule property of F-closure implies that F is closed. Moreover, if F is inductive, then F is a topological filter if and only if ClM F (A) is an intuitionistic fuzzy submodule for any intuitionistic fuzzy submodule A of M.

Prime Fuzzy Ideals of a Gamma Semiring -1

Prime Fuzzy Ideals of a Gamma Semiring -1

Left and Right Operator Rings of a Γ Ring in Terms of Rough Fuzzy Ideals

The relationship between Rough Set (RS) and algebraic systems has been long studied by mathematicians. RS is a growing research area that encourages studies into both real-world applications and the theory itself. In RS, a universe subset is characterized by a pair of ordinary sets called lower and upper approximations. In this study, we look attentively at the use of rough sets when the universe set has a ring structure. The main contribution of the paper is to concentrate on the study of rough fuzzy ideals concerning the gamma ring and to describe some properties of its lower and upper approximations. This paper deals with the connection between Rough Fuzzy Sets (RFS) and ring theory. The goal of this paper is to present the notion of Left Operator Rings (LOR) and Right Operator Rings (ROR) in the gamma ring structure. We introduce some basic concepts of rough fuzzy left and right operator rings. Furthermore, we investigate some characterizations of left and right operator rings and prove some theorems based on these results.

Characterizations of generalized fuzzy ideals in ordered semigroups

Ideals play an essential part in studying ordered semigroups. There are several generalizations of ideals that are used to investigate ordered semigroups. It is known that (m, n)-ideals are an abstraction of bi-ideals, and n-interior ideals are an abstraction of interior ideals. This paper introduces a generality of (m, n)-ideals and n-interior ideals, so-called (α, β)-fuzzy (m, n)-ideals and (α, β)-fuzzy n-interior ideals. Furthermore, we discuss our current notions with those that already exist. We examine connections between (m, n)- (resp., n-interior) ideals and (α, β)-fuzzy (m, n)- (resp., n-interior) ideals. A characterization of (α, β)-fuzzy (m, n)- (resp., n-interior) ideals, by a particular product, in ordered semigroups is provided. We demonstrate that our results generalize the known results through specific settings.

Application of Bipolar Fuzzy Set to a Novel of Fuzzy Ideal in $\Gamma$-Semigroups

In this paper we define new types of bipolar fuzzy ideals, bipolar fuzzy almost ideals in $\Gamma$-semigroups. We discussed properties of bipolar fuzzy ideals, bipolar fuzzy almost ideals, minimal bipolar fuzzy ideal, minimal bipolar almost ideal in $\Gamma$-semigroups. Moreover, we prove connection between almost ideals and bipolar fuzzy almost ideals of $\Gamma$-semigroups.

On Complete Intuitionistic Fuzzy Roh-Ideals in Roh-Algebras

In this paper, we shall investigate and study some kinds of ideals in an intuitionistic fuzzy setting, they are called complete intuitionistic fuzzy subalgebra, complete intuitionistic fuzzy ideal, and complete intuitionistic fuzzy ideal. In this study, we have also proposed some hypotheses to explain some of the relationships between these kinds of intuitionistic fuzzy ideals.