(untitled) (European Journal of Pure and Applied Mathematics, 2025)
In this paper, we introduce the concept of anti-fuzzy soft Boolean rings (AFSBRs), which serve as a complementary extension to fuzzy soft Boolean rings. While fuzzy soft structures have proven effective in modeling uncertainty through degrees of membership, they often overlook the critical role of non-membership or rejection—an essential aspect in contexts involving con- tradictions, conflict resolution, or decision-making under opposition. Motivated by this gap, the anti-fuzzy soft approach emphasizes the non-membership aspects of elements under uncertainty, offering a dual and more balanced perspective. We formally define the structure of AFSBRs, present basic operations, and explore their fundamental properties through illustrative examples and closure theorems. This study not only deepens the understanding of fuzzy algebraic systems but also provides a robust algebraic framework for modeling negative information in areas such as computational logic, artificial intelligence, and soft computing.