Pre A∗-Algebras and Their Applications in Fuzzy Set Theory

Gebregziabiher Girum Gebreset, Jonnalagadda Venkateswara Rao and Habtu Alemayehu Atsbaha

International Journal of Mathematics and Mathematical Sciences, 2026, vol. 2026, 1-9

Abstract: This paper studies Pre A∗-algebras and their role as an algebraic foundation for fuzzy set theory. By relaxing the key Boolean axioms of distributivity and complementation, Pre A∗-algebras provide a robust algebraic structure for reasoning with uncertainty. We construct a fundamental three-element algebra, A=0,1,2, representing truth, falsity, and an absorbing indeterminacy. We demonstrate how this structure models fuzzy membership and establishes clear links with standard logical connectives, including t-norms, t-conorms, fuzzy negation, and a multivalued XOR. Applications in decision-making, data processing, and fuzzy control illustrate the relevance of Pre A∗-algebras as a distinct and advantageous basis for multivalued systems.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:8543680

DOI: 10.1155/ijmm/8543680

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