(Fuzzy) Ideals of BN-Algebras

In this paper, we apply the concept of fuzzy set to ideals and closed ideals in B-algebras. The notion of a fuzzy closed ideal of a B-algebra is introduced, and some related properties are investigated. Also, the product of fuzzy B-algebra is investigated.

International Journal of Mathematics Trends and Technology, 2016

The concept of fuzzy ideals in BEalgebra have been introduced by Y. B. Jun, K. J. Lee and S. Z. Song in 2008-09. They investigated characteristic property of a fuzzy ideal and developed several properties. Here we study the concept of fuzzy ideals in Cartesian product of BEalgebra and the BEalgebra of all functions defined on a BEalgebra.

The aim of this paper is to introduce the notion of Doubt fuzzy ideals of BF -algebra and to investigate some of their basic properties.

European Journal of Pure and Applied Mathematics

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.

INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH

The main aim of this paper is to introduce the new concept of neutrosophic fuzzy bi-ideal of BS-algebras. Some algebraic nature are investigated. Neutrosophic fuzzy bi-ideal of BS-algebras is also applied in Cartesian product. Finally, we also provide the homomorphic behaviour of neutrosophic fuzzy bi-ideal of BS-algebras.

International Journal of Analysis and Applications

The notions of bipolar fuzzy closed, bipolar fuzzy positive implicative, bipolar fuzzy implicative ideals of BCK-algebras are introduced, and related properties are investigated. Characterizations of a closed, bipolar fuzzy positive implicative, bipolar fuzzy implicative ideals of BCK-algebras are given, and several properties are discussed. Finally, we prove that if T is an implicative BCK-algebra, then a fuzzy subset µ of T is a bipolar fuzzy ideal of T if and only if it is a bipolar fuzzy implicative ideal of T .

Computers & Mathematics with Applications, 2010

A generalization of an (∈, ∈ ∨q)-fuzzy ideal of a BCK/BCI-algebra is discussed. Characterizations of an (∈, ∈ ∨q k)-fuzzy ideal and an (∈, ∈∨q k)-fuzzy ideal are provided. Conditions for an (∈, ∈ ∨q k)-fuzzy ideal (resp. (∈, ∈ ∨ q k)-fuzzy ideal) to be a fuzzy ideal are provided. Using the notion of a fuzzy ideal with thresholds, characterizations of a fuzzy ideal, an (∈, ∈ ∨q k)-fuzzy ideal and an (∈, ∈ ∨ q k)-fuzzy ideal are discussed.

IAEME, 2019

In this paper we introduce the notions of Fuzzy Ideals in BH-algebras and the notion of fuzzy dot Ideals of BH-algebras and investigate some of their results

2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), 2013

The main goal of this paper is to investigate the properties of fuzzy ideals of a ring R. It provides a proof that there exists an isomorphism of lattices of fuzzy ideals when ever the rings are isomorphic. Finite-valued fuzzy ideals are also described and a method is created to count the number of fuzzy ideals in finite and Artinian rings.

We introduce the notion of normal fuzzy BCC-ideals, maximal fuzzy BCC-ideals and completely normal fuzzy BCC-ideals in BCC-algebras. We investigate some properties of normal (resp. maximal, completely normal) BCC-ideals. We show that every non-constant normal fuzzy BCCideal which is a maximal element of (N (X), ⊆) takes only the values 0 and 1, and every maximal fuzzy BCC-ideal is completely normal. 1991 AMS Subject Classication: 06F35, 03G25, 94D05