ALGEBRAIC HYPERSTRUCTURES ENHANCED BY FUZZY LOGIC USING THE ADVANCED THEORETICAL PERSPECTIVES

Abstract

This paper investigates the integration of fuzzy logic with algebraic hyperstructures, expanding the traditional framework of algebraic systems to address uncertainties and complexities inherent in real-world eventualities. Algebraic hyperstructures, which generalize conventional algebraic operations with the aid of making an allowance for multi-valued relationships, are more advantageous through fuzzy good judgment's capability to deal with partial truths and uncertainty. By making use of fuzzy common sense to hyperstructures, we introduce new constructs such as fuzzy hyperoperations and fuzzy hypergroups, which give a extra bendy and nuanced method to algebraic modeling.

We present a complete theoretical analysis of these fuzzy-greater algebraic hyperstructures, exploring their homes, balance, and interactions with classical algebraic structures. Our studies not handiest establishes foundational consequences however additionally demonstrates practical packages in computational algebra, optimization, and choice-making approaches. This integration provides full-size advancements in understanding and making use of algebraic structures to complex, unsure problems, highlighting the ability of mixing fuzzy logic with algebraic hyperstructures for progressed theoretical and realistic results.