The notions of m-polar fuzzy subalgebras and m-polar fuzzy (closed, commutative) ideals are introduced, and related properties are investigated. Characterizations of m-polar fuzzy subalgebras and m-polar fuzzy (commutative) ideals are considered. Relations between m-polar fuzzy subalgebras, m-polar fuzzy ideals and m-polar fuzzy commutative ideals are discussed.

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 $BCK/BCI$ -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 $(\alpha ,\beta )$ -fuzzy ideals in $BCK/BCI$ -algebras. The defined notion is a generalization of fuzzy ideals, bipolar fuzzy ideals, $(\alpha ,\beta )$ -fuzzy ideals, and bipolar $(\alpha ,\beta )$ -fuzzy ideals in $BCK/BCI$ -algebras. We describe the characterization of m-polar $(\in ,\in \vee q)$ -fuzzy ideals in $BCK/BCI$ -algebras by level cut subsets. Moreover, we define m-polar $(\in ,\in \vee q)$ -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.

The concept of complex fuzzy sets, where the unit disk of the complex plane acts as the codomain of the membership function, as an extension of fuzzy sets. The objective of this article is to use complex fuzzy sets in BCK/BCI-algebras. We present the concept of a complex fuzzy subalgebra in a BCK/BCI-algebra and explore their properties. Furthermore, we discuss the modal and level operators of these complex fuzzy subalgebras, highlighting their importance in BCK/BCI-algebras. We study various operations, and the laws of a complex fuzzy system, including union, intersection, complement, simple differences, and bounded differences of complex fuzzy ideals within BCK/BCI-algebras. Finally, we generate a computer programming algorithm that implements our complex fuzzy subalgebras/ideals in BCK/BCI-algebras procedure for ease of lengthy calculations.

In this paper, we introduce some new concepts of fuzzy soft graphs with the notions of complement and μ-complement fuzzy soft graphs introduced. Investigating some of their properties, we show that the complement of strong fuzzy soft graph is strong fuzzy soft one as well as the complement of a complete fuzzy soft graph is complete fuzzy soft one. Finally, we state and prove some results related to these concepts

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.