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Multi-polar vagueness in data plays a prominent role in several areas of the sciences. In recent years, the thought of m-polar fuzzy sets has captured the attention of numerous analysts, and research in this area has escalated in the past four years. Hybrid models of fuzzy sets have already been applied to many algebraic structures, such as B C K / B C I -algebras, lie algebras, groups, and symmetric groups. A symmetry of the algebraic structure, mathematically an automorphism, is a mapping of the algebraic structure onto itself that preserves the structure. This paper focuses on combining the concepts of m-polar fuzzy sets and m-polar fuzzy points to introduce a new notion called m-polar ( α , β ) -fuzzy ideals in B C K / B C I -algebras. The defined notion is a generalization of fuzzy ideals, bipolar fuzzy ideals, ( α , β ) -fuzzy ideals, and bipolar ( α , β ) -fuzzy ideals in B C K / B C I -algebras. We describe the characterization of m-polar ( ∈ , ∈ ∨ q ) -fuzzy ideals in B C K / B C I -algebras by level cut subsets. Moreover, we define m-polar ( ∈ , ∈ ∨ q ) -fuzzy commutative ideals and explore some pertinent properties.

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.

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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.