An Investigation into Bipolar Fuzzy Hoop Algebras and Their Applications
Tahsin Öner, Rajesh Neelamegarajan, Ravikumar Bandaru, Hashem Bordbar · Axioms · 2025
This paper introduces bipolar fuzzy sub-hoops and bipolar fuzzy filters within hoop algebras, extending fuzzy logic to incorporate both positive and negative membership degrees. We define these structures, explore their algebraic properties, and establish their interplay through rigorous theorems. Key results include characterizations of bipolar fuzzy filters via level sets and conditions under which they become implicative filters. These findings enhance the theoretical framework of many-valued logic and offer practical applications in decision-making, image processing, and spatial reasoning under uncertainty. Our work provides a foundation for advanced fuzzy systems handling complex, contradictory information.