FUZZY IDEALS AND FUZZY DOT IDEALS ON BH-ALGEBRAS

2014

In this paper, the notions of fuzzy dot subalgebras, fuzzy normal dot subalgebras and fuzzy dot ideals of B-algebras are introduced and investigated some of their properties. The homomorphic image and inverse image of fuzzy dot subalgebras and fuzzy dot ideals are studied. Also introduced the notion of fuzzy relations on the family of fuzzy dot subalgebras and fuzzy dot ideals of B-algebras and investigated some related properties. c ©2014 World Academic Press, UK. All rights reserved.

2000

Abstract. We introduce the notion of fuzzy dot subalgebras in BCH-algebras, and study its various properties. 2000 Mathematics Subject Classification. 06F35, 03G25, 03E72. 1. Introduction. In [4], Hu and Li introduced the notion of BCH-algebras which are a generalization of BCK/BCI-algebras. In 1965, Zadeh [6] introduced the concept of fuzzy subsets. Since then several researchers have applied this notion to various mathematical disciplines. Jun [5] applied it to BCH-algebras, and he considered the fuzzification of ideals and filters in BCH-algebras. In this paper, we introduce the

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.

In this paper, we study the notion of fuzzy sub-implicative ideal of a BH-algebra and we state and prove some theorems and propositions which determine the relationships among the sub-implicative ideal with the other subset in fuzzy senses of BH-algebra and also we give some properties of this ideal and relate it with other types of concepts of a BH-algebra.

International Journal of Mathematics and Mathematical Sciences, 2001

We introduce the notion of fuzzy dot subalgebras in BCH-algebras, and study its various properties.

The Scientific World Journal, 2015

The notions of an ideal and a fuzzy ideal in BN-algebras are introduced. The properties and characterizations of them are investigated. The concepts of normal ideals and normal congruences of a BN-algebra are also studied, the properties of them are displayed, and a one-to-one correspondence between them is presented. Conditions for a fuzzy set to be a fuzzy ideal are given. The relationships between ideals and fuzzy ideals of a BN-algebra are established. The homomorphic properties of fuzzy ideals of a BN-algebra are provided. Finally, characterizations of Noetherian BN-algebras and Artinian BN-algebras via fuzzy ideals are obtained.

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.

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 Mathematical Forum, 2010

The notion of an T H-interval-valued fuzzy BH-subalgebra in a BHalgebra is introduced, and related properties are investigated.

European Journal of Pure and Applied Mathematics, 2018

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.