An Innovative Method for Employing Complex Intuitionistic Fuzzy Ideals in $\mathcal{B}\mathcal{C}\mathds{K}/ \mathcal{B}\mathcal{C}\mathcal{I}$-Algebras (European Journal of Pure and Applied Mathematics, 2025)
The complex intuitionistic fuzzy set is a more generalized version of the complex fuzzy set. It is made by including the complex degree of non-grading functions, which are also important in the decision-making process, and studying their basic properties. The complex intuitionistic fuzzy set extends theories like the complex fuzzy set, intuitionistic fuzzy set, and fuzzy set. The goal of this paper is to apply complex intuitionistic fuzzy sets in $\mathcal{B}\mathcal{C}\mathds{K}/ \mathcal{B}\mathcal{C}\mathcal{I}$-algebras ($M$), explain what a complex intuitionistic fuzzy ideal is, and explore some of its properties. We introduce the notion of a complex intuitionistic fuzzy sub-algebra in $M$, and its characteristics are investigated. We also look into the level operators and models of these complex intuitionistic fuzzy sub-algebras and explain their importance in $M$. Finally, we discuss the laws and operations of a complex intuitionistic fuzzy set in $M$, such as complement, intersection, union, boundedness, and simple differences of complex intuitionistic fuzzy ideals.
Keywords: complex intuitionistic fuzzy sub-algebra; complex intuitionistic fuzzy environment; fuzzy logic; $\mathcal{B}\mathcal{C}\mathds{K}/ \mathcal{B}\mathcal{C}\mathcal{I}$-algebras