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Mshelia, Bello Inuwa
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Mathematics

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Axiomatization of a Fundamental System for Generalized Ambiguous Four–Degree Membership Function Set Theory Aji, Ali; Mshelia, Bello Inuwa; Haruna, Yusuf
Eigen Mathematics Journal Vol 9 No 1 (2026): June
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v9i1.356

Abstract

This paper presents the construction of an axiomatic system of Generalized Ambiguous Set Theory (AGAST)founded upon a four-valued logic, where the membership relation accepts four discrete degrees: True $(\alpha_A (x))$, Partially True $(\beta_A (x))$, Partially False $(\gamma_A (x))$, and Falsity $(\eta_A (x))$ membership degree functions, The contribution of this work is the rigorous adaptation of foundational Zermelo-Frankel set theory (ZFC) and Axiomatic Fuzzy Set Theory principles, including the Axiom of Extensionality and the Axiom Schema of Ambiguous Separation, to cohere within the four-degree semantics. Furthermore, the theory introduces the Anti-Classicality Axiom, which postulates the existence of sets exhibiting non-classical membership degrees.
Co-Authors Aji, Ali Yusuf Haruna