In this paper, we investigate anti-fuzzy primary ideals in the setting of (m, n) -near rings. We study their basic properties and present several characterizations that describe their algebraic structure. The relationships between anti-fuzzy primary ideals and classical primary ideals in (m, n) -near rings are examined, as well as their connections with other classes of anti-fuzzy ideals. Moreover, we analyze the behavior of anti-fuzzy primary ideals under (m, n) -near ring homomorphisms and prove that, under suitable conditions, their homomorphic images and preimages preserve primary-type properties. These results extend existing theories of fuzzy and anti-fuzzy ideals to the broader framework of (m, n) -near rings and provide further insight into their ideal structure.
Mohammadi et al. (Thu,) studied this question.
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