Anti fuzzy implicative ideals in BCK-algebras

Fuzzy Sets and Systems, 1997

In this paper, we introduce the concept of fuzzy implicative ideals in BCK-algebras and study some of their properties.

Fuzzy Sets and Systems, 1997

In this paper we study further properties of fuzzy implicative ideals, and construct a fuzzy characteristic implicative ideal in BCK-algebras.

Journal of Mathematics, 2021

The notion of bipolar fuzzy implicative ideals of a BCK-algebra is introduced, and several properties are investigated. The relation between a bipolar fuzzy ideal and a bipolar fuzzy implicative ideal is studied. Characterizations of a bipolar fuzzy implicative ideal are given. Conditions for a bipolar fuzzy set to be a bipolar fuzzy implicative ideal are provided. Extension property for a bipolar fuzzy implicative ideal is stated.

Bulletin of the Korean Mathematical Society, 2006

As a continuation of , characterizations of fuzzy implicative ideals are given. An extension property for fuzzy implicative ideals is established. We prove that the family of fuzzy implicative ideals is a completely distributive lattice. Using level subsets of a BCK-algebra X with respect to a fuzzy setĀ in X, we construct a fuzzy implicative ideal of X containingĀ.

Journal of Algebraic Hyperstructures and Logical Algebras

In BCK-algebras, the notion of Łukasiewicz fuzzy positive implicative ideal is introduced, and several properties are investigated. The relationship between Łukasiewicz fuzzy ideal and Łukasiewicz fuzzy positive implicative ideal is discussed, and characterizations of a Łukasiewicz fuzzy positive implicative ideal are considered. Conditions for a Łukasiewicz fuzzy ideal to be a Łukasiewicz fuzzy positive implicative ideal are provided, and conditions for the ∈-set, q-set and O-set to be positive implicative ideals are explored.

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 .

Journal of Mathematics

This study focuses on combining the theories of m -polar fuzzy sets over BCK -algebras and establishing a new framework of m -polar fuzzy BCK -algebras. In this paper, we define the idea of m -polar fuzzy positive implicative ideals in BCK -algebras and investigate some related properties. Then, we introduce the concepts of m -polar ∈ , ∈ ∨ q -fuzzy positive implicative ideals and m -polar ∈ ¯ , ∈ ¯ ∨ q ¯ -fuzzy positive implicative ideals in BCK -algebras as a generalization of m -polar fuzzy positive implicative ideals. Several properties, examples, and characterization theorems of these concepts are considered.

Journal of Intelligent & Fuzzy Systems, 2019

Fuzzy soft set theory is applied to hyper BCK-algebras. The notion of fuzzy soft positive implicative hyper BCK-ideals is introduced, and several properties are investigated. The relation between fuzzy soft positive implicative hyper BCK-ideal and fuzzy soft hyper BCK-ideal is considered. Characterizations of fuzzy soft positive implicative hyper BCKideal are provided. Using the notion of positive implicative hyper BCK-ideal, a fuzzy soft weak (strong) hyper BCK-ideal is established.

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.

Journal of Applied Mathematics and Computing, 2003

The fuzzification of (positive implicative) pseudo-ideals in a pseudo-BCK algebra is discussed, and several properties are investigated. Characterizations of a fuzzy pseudo-ideal are displayed.