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

Author

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  • Gebregziabiher Girum Gebreset
  • Jonnalagadda Venkateswara Rao
  • Habtu Alemayehu Atsbaha

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.

Suggested Citation

  • Gebregziabiher Girum Gebreset & Jonnalagadda Venkateswara Rao & Habtu Alemayehu Atsbaha, 2026. "Pre A∗-Algebras and Their Applications in Fuzzy Set Theory," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2026, pages 1-9, September.
    • Handle: RePEc:hin:jijmms:8543680
    DOI: 10.1155/ijmm/8543680
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