Abstract
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.
Highlights
E essential idea of a fuzzy set, proposed by Zadeh [2] in 1965, provides a natural framework for generalizing many fundamental concepts of algebras
The idea of fuzzy sets in BCK/BCI-algebras was proposed by Xi [3]. e theory of fuzzy algebraic structures plays a prominent role in different domains of mathematics and other sciences such as theoretical physics, topological spaces, real analysis, coding theory, set theory, logic, and information sciences
In 1994, bipolar fuzzy (BF) set theory was proposed by Zhang [4] as a new platform that extends crisp and fuzzy sets
Summary
E essential idea of a fuzzy set, proposed by Zadeh [2] in 1965, provides a natural framework for generalizing many fundamental concepts of algebras. Motivated by a lot of work on m-pF sets, we present m-polar fuzzy positive implicative (m-pFPI) ideals in BCK-algebras and discuss some related results. An m-pF set MP of Ω is an m-pFPI ideal of Ω if and only if MPξ ≠ φ is a positive implicative ideal of Ω for all ξ ∈
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