Bipolar complex fuzzy near rings

Abstract In this article, we devise the novel concept of bipolar complex fuzzy (BCF) near rings (BCFNR), to fill a momentous research gap in connection of bipolar complex fuzzy sets with the theory of near rings in the existing literature. We expand the theory of near ring into the structure of BCF set (BCFS), offering a more suitable approach for the representation of algebraic systems with inherent ambiguity, bipolarity, and 2nd dimension information. Further, we introduce the concept of the bipolar complex fuzzy sub-near ring (BCFSNR), bipolar complex fuzzy left ideal (BCFLI), bipolar complex fuzzy right ideal (BCFRI), and bipolar complex fuzzy ideal (BCFI) in the near ring. After that, we prove the related theorem and results of these devised concepts. We also introduce theorems based on the homomorphism theory and Noetherian theory of near rings within the frame of bipolar complex fuzzy near rings. At the end of the manuscript, we reveal the application of BCFNRs in decision-making (DM) and illustrate it through an example.