Fuzzy Subalgebras Research Articles

On Some Properties of Doubt Bipolar Fuzzy H-ideals in BCK/BCI-algebras

In this research article, we study some properties of doubt bipolar fuzzy H-ideals inBCK/ BCI-algebras. Doubt bipolar fuzzy H-ideals are connected with doubt bipolar fuzzy subalgebras and doubt bipolar fuzzy ideals. Moreover, doubt bipolar fuzzy H-ideals are characterized using doubt positive t-level cut set, doubt negative s-level cut set and H-Artin BCK/BCI-algebras.

Neutrosophic Hesitant Fuzzy Subalgebras and Filters in Pseudo-BCI Algebras

The notions of the neutrosophic hesitant fuzzy subalgebra and neutrosophic hesitant fuzzy filter in pseudo-BCI algebras are introduced, and some properties and equivalent conditions are investigated. The relationships between neutrosophic hesitant fuzzy subalgebras (filters) and hesitant fuzzy subalgebras (filters) is discussed. Five kinds of special sets are constructed by a neutrosophic hesitant fuzzy set, and the conditions for the two kinds of sets to be filters are given. Moreover, the conditions for two kinds of special neutrosophic hesitant fuzzy sets to be neutrosophic hesitant fuzzy filters are proved.

On interval valued intuitionistic fuzzy $$\beta $$ β -subalgebras

This paper deals the notion of interval valued instuitionistic fuzzy subalgebras of $$\beta $$ -algebra and investigate some of the related results.

(∈,∈∨q)-Fuzzy Subalgebras and Fuzzy Ideals of BCI-Algebras with Operators

(∈,∈∨q)-Fuzzy Subalgebras and Fuzzy Ideals of BCI-Algebras with Operators

$(\in,\in\vee q)$-bipolar Fuzzy $BCK/BCI$-algebras

In this paper, the concept of quasi-coincidence of a bipolar fuzzy point within a bipolar fuzzy set is introduced. The notion of $(\in,\in\vee q)$-bipolar fuzzy subalgebras and ideals of $BCK/BCI$-algebras are introduced and their related properties are investigated by some examples. We study bipolar fuzzy $BCK/BCI$-subalgebras and bipolar fuzzy $BCK/BCI$-ideals by their level subalgebras and level ideals. We also provide the relationship between $(\in,\in\vee q)$-bipolar fuzzy $BCK/BCI$-subalgebras and bipolar fuzzy $BCK/BCI$-subalgebras, and $(\in,\in\vee q)$-bipolar fuzzy $BCK/BCI$-ideals and bipolar fuzzy $BCK/BCI$-ideals by counter examples.

A new type of hesitant fuzzy subalgebras and ideals in BCK/BCI-algebras

A new type of hesitant fuzzy subalgebras and ideals in BCK/BCI-algebras

Fuzzy n-Lie Algebras

Properties of fuzzy subalgebras and ideals of n-ary Lie algebras are described. Methods of construction fuzzy ideals are presented. Connections with various fuzzy quotient n-Lie algebras are proved.

Some drifts on posets and its application to fuzzy subalgebras

In this paper, given a poset $(X,leq)$, we introduce some drifts on a groupoid $(X,*)$ with respect to $(X,leq)$, and we obtain several properties of these drifts related to the notion of $Bin(X)$. We discuss some connections between fuzzy subalgebras and upward drifts.

On some properties of p-ideals based on intuitionistic fuzzy sets

In this paper, we consider the intuitionistic fuzzification of the concept of p-ideals in BCI-algebras and investigate some of their properties. Intuitionistic fuzzy p-ideals are connected with intuitionistic fuzzy ideals and intuitionistic fuzzy subalgebras. Moreover, intuitionistic fuzzy p-ideals are characterized using level subsets, homomorphic pre-images, and intuitionistic fuzzy ideal extensions.

Some properties of n-dimensional (∈γ, ∈γ, ∨qδ)-fuzzy subalgebra in BRK-algebras

Abstract The purpose of this paper is to initiate the concept of n-dimensional (∈γ, ∈γ, ∨qδ)-fuzzy subalgebra in BRK-algebra and investigate some of their related properties. We also show that the relationship between n-dimensional (∈γ, ∈γ, ∨qδ)-fuzzy subalgebra and the crisp subalgebra in BRK-algebra are discussed.

Fuzzy translations and fuzzy multiplications of interval-valued doubt fuzzy ideals of BF-algebras

In this paper, we introduced the concept of fuzzy translations and fuzzy multiplications of interval-valued doubt fuzzy ideals and interval-valued doubt fuzzy subalgebras of BF-algebra and investigated some of their basic properties.

Translations of Intuitionistic Fuzzy [formula omitted]-algebras

In this paper, the concept of intuitionistic fuzzy translation to intuitionistic fuzzy subalgebras and ideals in B-algebras are introduced with several related properties investigated. Examples are also given to illustrate results. The notion of intuitionistic fuzzy extensions and intuitionistic fuzzy multiplications of intuitionistic fuzzy subalgebras and ideals are introduced. Relationships are investigated between intuitionistic fuzzy translations, intuitionistic fuzzy extensions and intuitionistic fuzzy multiplications of intuitionistic fuzzy subalgebras and ideals.

Triangular norm based fuzzy $$BG$$ B G -algebras

In this paper, using \(t\)-norm \(T\), the notion of (imaginable) \(T\)-fuzzy subalgebras and (imaginable) \(T\)-fuzzy closed ideals of \(BG\)-algebras are introduced and investigated their related results. Relationship between an imaginable \(T\)-fuzzy subalgebra and an imaginable \(T\)-fuzzy closed ideal are given. The direct product and \(T\)-product of \(T\)-fuzzy subalgebras of \(BG\)-algebras are discussed.

Characterizations of fuzzy subalgebras in BCK/BCI-algebras

The concepts of (∈, ∈ ∨ qδ 0)-fuzzy subalgebras and ∈ ∨ qδ 0-level sets Corresponding author 7188 G. Muhiuddin, Seok Zun Song, Hee Sik Kim, Young Bae Jun are introduced, and related properties are investigated. Relations between an (∈,∈)-fuzzy subalgebra and an (∈, ∈ ∨ qδ 0)-fuzzy subalgebra are discussed, and characterizations of (∈, ∈∨ qδ 0)-fuzzy subalgebras are discussed. Homomorphic image and pre-image of an (∈, ∈ ∨ qδ 0)-fuzzy subalgebra are considered. Mathematics Subject Classification: 06F35, 03G25, 08A72

Intuitionistic Fuzzy Subbialgebras and Duality

We investigate connections between bialgebras and Atanassov’s intuitionistic fuzzy sets. Firstly we define an intuitionistic fuzzy subbialgebra of a bialgebra with an intuitionistic fuzzy subalgebra structure and also with an intuitionistic fuzzy subcoalgebra structure. Secondly we investigate the related properties of intuitionistic fuzzy subbialgebras. Finally we prove that the dual of an intuitionistic fuzzy strong subbialgebra is an intuitionistic fuzzy strong subbialgebra.

Fuzzy identities with application to fuzzy semigroups

The notion of a fuzzy identity is introduced on a fuzzy subalgebra in the framework of fuzzy equalities instead of the crisp one. A fuzzy identity may be satisfied by a fuzzy subalgebra, while the underlying crisp algebra need not satisfy the analogous crisp identity. Among other properties, it is shown that for every fuzzy subalgebra μ of A there is a least fuzzy equality such that a fuzzy identity holds on μ. As an application, fuzzy semigroups are introduced with respect to a fuzzy equality. In particular, fuzzy semilattices, cancellative and regular fuzzy semigroups are investigated.

FUZZY EQUATIONAL CLASSES ARE FUZZY VARIETIES

In the framework of fuzzy algebras with fuzzy equalities and a complete lattice as a structure of membership values, we investigate fuzzy equational classes. They consist of special fuzzy algebras fullling the same fuzzy identities, dened with respect to fuzzy equalities. We introduce basic notions and the corresponding operators of universal algebra: construction of fuzzy subalgebras, homomorphisms and direct products. We prove that every fuzzy equational class is closed under these three operators, which means that such a class is a fuzzy variety.

Fuzzy B-subalgebras of B-algebra with Respect to t-norm

In this paper, we apply the concept of $t-$norm $T$ to fuzzy structure of $B-$algebras. The notion of a fuzzy $B-$subalgebra of $B-$algebras with respect to $t-$norm is introduced and several related properties are investigated. The direct product and $T-$product of $T-$fuzzy subalgebra of $B-$algebra is investigated.

Intuitionistic [formula omitted]-fuzzy [formula omitted]-algebras

In this paper, we introduce the notion of intuitionistic ( T , S ) -fuzzy subalgebras in C I -algebras and study their fundamental properties. We get a fuzzy subalgebra from an intuitionistic ( T , S ) -fuzzy subalgebra. Also the notion of intuitionistic ( T , S ) -fuzzy (closed) filters of C I -algebras is introduced. We investigate the relationship between intuitionistic ( T , S ) -fuzzy subalgebras and intuitionistic ( T , S ) -fuzzy (closed) filters of C I -algebras.

Fuzzy soft ideals in subtraction algebras

In this article, we introduced the notions fuzzy soft subalgebras and fuzzy soft ideal of subtraction algebras. We showed that fuzzy soft image and fuzzy soft inverse image of fuzzy soft ideal are both fuzzy soft ideal under certain conditions. We have studied their related properties in details.