Abstract
In 2020, Kang et al. introduced the concept of a multipolar intuitionistic fuzzy set of finite degree, which is a generalization of a k-polar fuzzy set, and applied it to a BCK/BCI-algebra. The specific purpose of this study was to apply the concept of a multipolar intuitionistic fuzzy set of finite degree to a hyper BCK-algebra. The notions of the k-polar intuitionistic fuzzy hyper BCK-ideal, the k-polar intuitionistic fuzzy weak hyper BCK-ideal, the k-polar intuitionistic fuzzy s-weak hyper BCK-ideal, the k-polar intuitionistic fuzzy strong hyper BCK-ideal and the k-polar intuitionistic fuzzy reflexive hyper BCK-ideal are introduced herein, and their relations and properties are investigated. These concepts are discussed in connection with the k-polar lower level set and the k-polar upper level set.
Highlights
As is well known, the fuzzy set, which was first introduced by Zadeh [1], dealt with the membership degree that is represented by only one function, the so-called truth function
Introduced an m-polar fuzzy set which is an extension of the bipolar fuzzy set, and this notion was applied to graph theory, algebraic structure, the decision making problem, etc
In [15], Kang et al introduced the concept of a multipolar intuitionistic fuzzy set of finite degree as a generalization of an intuitionistic fuzzy set, and they applied it to BCK/BCI-algebras
Summary
The fuzzy set, which was first introduced by Zadeh [1], dealt with the membership degree that is represented by only one function, the so-called truth function. Introduced an m-polar fuzzy set which is an extension of the bipolar fuzzy set, and this notion was applied to graph theory, algebraic structure, the decision making problem, etc. In [15], Kang et al introduced the concept of a multipolar intuitionistic fuzzy set of finite degree as a generalization of an intuitionistic fuzzy set, and they applied it to BCK/BCI-algebras. Applied the hyperstructure theory to BCK-algebras, and they introduced a hyper BCK-algebra which is a generalization of a BCK-algebra They studied hyper ideal theory in hyper BCK-algebras. Xin discussed the fuzzy set theory of hyper BCK-ideals in hyper BCK-algebras (see [19]), and Bakhshi et al [20] studied fuzzy (positive, weak) implicative hyper BCK-ideals. We discuss k-pIF (weak, s-weak, strong, reflexive) the hBCK-ideal in relation to k-polar upper and lower level sets
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