This paper investigates the categorical framework for generalized multi-dimensional fuzzy sets, extending Zadeh’s original theory. We introduce a generalized variant where the co-domain is a partially ordered set. Fundamental categorical notions such as initial and terminal objects, separators, co-separators, and various morphisms (e.g., mono-, epi-, iso-, section, and retraction) are explored. We prove the category is complete and co-complete by identifying equalizers, co-equalizers, products, and co-products using new union and intersection operations for these sets.