Bipolar Intuitionistic Anti Fuzzy 𝛼-Ideal of A BP-Algebra

Objectives: The focus of this article is to present the idea of employing complement, union, and intersection and examine these fundamental operations in both bipolar intuitionistic anti fuzzy (BIAF) ideals. We investigate the conditions of BIAF ideal and BIAF α-ideal of a BP-algebra in this research work. Comparing the fuzzy set to a bipolar intuitionistic fuzzy set revealed a definite result. Therefore, the concept of bipolar intuitionistic fuzzy set was defined as a combination of intuitionistic fuzzy set and bipolar fuzzy set. It provides useful outcomes for problem analysis. Methods: We provide the conditions for both BIAF ideals. We also give characterizations of a bipolar intuitionistic fuzzy (BIF) set. Findings: Implementing the fuzzy theory and ideal theory of a BP-algebra is the main aim of this study that can represent uncertainty and bipolarity in data. We consider the methodology as a concept of the BIAF ideals and discuss the operations. Novelty: The introduction of the BIAF ideals and the thorough examination of the basic operations constitute the research's uniqueness. In BIAF ideals, the study highlighted the concepts of complement, the union of two BIAF ideals and intersection of two BIAF ideals that can be investigated to provide more flexibility in analyzing problems. This study is easy to understand, very effective, and appropriate for novices in a variety of professions. In this article, BIAF ideals play the major role with some basic operations. 2020 MSC: 03E72, 08A72. Keywords: BP-Algebra, Fuzzy Ideal, Bipolar Fuzzy Ideal, BIAF Ideal, BIAF α-Ideal