On Anti Fuzzy Primary Ideals of an $(m, n)$-Near Ring

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.