Intuitionistic Multi‐Antifuzzy Normed Substructures Over Normed Rings

In this paper, we introduce new fuzzy algebraic structures on normed rings, namely, intuitionistic multi‐antifuzzy normed normal subrings (IMAFNNSRs) and the associated intuitionistic multi‐antifuzzy normed normal ideals (IMAFNNIs). In this context, we use t ‐ and s ‐norms to assign membership and nonmembership degrees. The standard fuzzy inequalities are reversed to define antifuzzy inequalities, which characterize exclusion‐based behavior. The study shows that IMAFNNSRs are closed under intersection and can be characterized by intuitionistic multi‐antifuzzy characteristic functions. Comparable results are obtained for IMAFNNIs, where the multiplicative conditions are modified to obtain the ideal absorption property within the antifuzzy framework. Moreover, the proposed formulations are shown to be stable under direct product structures of normed rings. Several illustrative examples involving parity and residue classes are presented to demonstrate the applicability of the suggested framework to multiple antifuzzy attributes. The framework thus provides a rigorous mathematical foundation for modeling exclusion‐oriented, multicriteria uncertainty, with potential applications in information fusion, access control, and multiattribute decision‐making.