DOUBT INTUITIONISTIC FUZZY IDEALS IN BCK/BCI-ALGEBRAS

International Journal of Fuzzy Logic Systems, 2015

In this paper, we introduce the concept of doubt intuitionistic fuzzy subalgebras and doubt intuitionistic fuzzy ideals in BCK/BCI-algebras. We show that an intuitionistic fuzzy subset of BCK/BCI-algebras is an intuitionistic fuzzy subalgebra and an intuitionistic fuzzy ideal if and only if the complement of this intuitionistic fuzzy subset is a doubt intuitionistic fuzzy subalgebra and a doubt intuitionistic fuzzy ideal. And at the same time we have established some common properties related to them.

2000

Abstract. We consider the intuitionistic fuzzification of the concept of subalgebras and ideals in BCK-algebras, and investigate some of their properties. We introduce the notion of equivalence relations on the family of all intuitionistic fuzzy ideals of a BCK-algebra and investigate some related properties.

International Journal of Mathematics and Mathematical Sciences, 2000

We consider the intuitionistic fuzzification of the concept of subalgebras and ideals in BCK-algebras, and investigate some of their properties. We introduce the notion of equivalence relations on the family of all intuitionistic fuzzy ideals of a BCK-algebra and investigate some related properties.

Applications and Applied Mathematics: An International Journal (AAM), 2020

Several generalizations and extensions of fuzzy sets have been introduced in the literature, for example, Atanassov's intuitionistic fuzzy sets, type 2 fuzzy sets and fuzzy multisets, etc. Using the Torra's hesitant fuzzy sets, the notions of Sup-hesitant fuzzy ideals in BCK/BCI-algebras are introduced, and its properties are investigated. Relations between Sup-hesitant fuzzy subalgebras and Sup-hesitant fuzzy ideals are displayed, and characterizations of Sup-hesitant fuzzy ideals are discussed.

2018

The notions of doubt bipolar fuzzy subalgebras and (closed) doubt bipolar fuzzy ideals are introduced, and related properties are investigated. Characterizations of a doubt bipolar fuzzy subalgebra and a doubt bipolar fuzzy ideal are given, and relations between a doubt bipolar fuzzy subalgebra and a doubt bipolar fuzzy ideal are discussed. The concepts of homomorphic preimages and doubt images of doubt bipolar fuzzy ideals in BCK/BCIalgebras are investigated. Conditions for a doubt bipolar fuzzy ideal to be a closed doubt bipolar fuzzy ideal are provided.

European Journal of Pure and Applied Mathematics

In the present paper, we introduce the notions of Inf-hesitant fuzzy subalgebras and Inf-hesitant fuzzy ideals in BCK/BCI-algebras and investigate their relations and properties. In addition, we discuss the characterizations of Inf-hesitant fuzzy subalgebras and Inf-hesitant fuzzy ideals in BCK/BCI-algebras.

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.

In this paper, the concepts of intuitionistic fuzzy translation to intuitionistic fuzzy Hideals in BCK/BCI-algebras are introduced. The notion of intuitionistic fuzzy extensions and intuitionistic fuzzy multiplications of intuitionistic fuzzy H-ideals with several related properties are investigated. Also the relationships between intuitionistic fuzzy translations, intuitionistic fuzzy extensions and intuitionistic fuzzy multiplications of intuitionistic fuzzy H-ideals are 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.

2020

Based on the hesitant fuzzy set theory which is introduced by Torra in the paper [12], the notions of Inf-hesitant fuzzy subalgebras, Inf-hesitant fuzzy ideals and Inf-hesitant fuzzy p-ideals in BCK/BCI-algebras are introduced, and their relations and properties are investigated. Characterizations of an Inf-hesitant fuzzy subalgebras, an Inf-hesitant fuzzy ideals and an Inf-hesitant fuzzy p-ideal are considered. Using the notion of BCK-parts, an Inf-hesitant fuzzy ideal is constructed. Conditions for an Inf-hesitant fuzzy ideal to be an Inf-hesitant fuzzy p-ideal are discussed. Using the notion of Inf-hesitant fuzzy (p-) ideals, a characterization of a p-semisimple BCI-algebra is provided. Extension properties for an Inf-hesitant fuzzy p-ideal is established.