On a New Category of Fuzzy Sets

We introduce the concept of a morphism between fuzzy sets, which enables us to define the category of fuzzy sets. Next, we give elementwise characterization of some special morphisms in this category which will be useful for later studies. We prove that unlike the category of sets, this category is not balanced. Also, we prove that this category has equalizers, coequalizers, intersections, images and weak inverse images.