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Complex fuzzy coverings (CFCs) are the natural mixture of the complex fuzzy sets (CFSs) and coverings, which are the modified versions of the coverings by replacing crisp sets with CFSs. This manuscript aims to explore the complex fuzzy neighborhood operators (CFNOs) by introducing the notions such as &#x03B2;-neighborhood system ( &#x03B2;-NO), complex fuzzy &#x03B2;-minimal description (CF &#x03B2;-MND), and complex fuzzy &#x03B2;-maximal description (CF &#x03B2;-MXD). First, we explore the complex fuzzy &#x03B2;-covering approximation space (CF &#x03B2;-CAS) and then we propose the above notions and investigate their properties. Additionally, we construct the CFNOs based on the complex fuzzy &#x03B2;-coverings (CF &#x03B2;-Cs). Finally, the CF &#x03B2;-Cs were derived by using CFNOs, and their properties are considered. These all notions are also verified with the help of suitable examples to show that the presented approaches are extensive, reliable, and proficient techniques.

Interdependency of Complex Fuzzy Neighborhood Operators and Derived Complex Fuzzy Coverings