On fundamental algebraic characterizations of complex intuitionistic Q-fuzzy subfield

The main objective of this study is to propose a new notion of a complex intuitionistic $Q$-fuzzy subfield of a field $F$ that is developed from the concept of a complex fuzzy subfield of a field $F$ by adding the notion of intuitionistic $Q$-fuzzy into a complex fuzzy subfield. We establish a new structure of complex fuzzy subfields which is called complex intuitionistic $Q$-fuzzy subfield. The most significant advantage of this addition appears to be that it broadens the scope of the investigation from membership function values to membership and non-membership function values. The range of complex fuzzy subfields is expanded to the unit disc in the complex plane for both membership and non-membership functions. Some fundamental operations, especially the intersection, union, and complement of complex intuitionistic $Q$-fuzzy subfields are studied. We define the necessity and possibility operators on a complex intuitionistic $Q$-fuzzy subfield. Moreover, we show that each complex intuitionistic $Q$-fuzzy subfield generates two intuitionistic $Q$-fuzzy subfields. Subsequently, several related theorems are proven.