فئة المجموعات المشوشة و تطبيقات مورفيزماتها الشاملة

Abstract EN

This paper introduces a generalization of the concept of Set category introduced in [10] by constructing the category LF-Set whose objects are small £ - fuzzy sets in which the characteristic functions takes its values from a complete distributive lattice, and its arrows are £ - fuzzy maps.

After that we construct a functor 0: CF-Set →Set between these two categories, in a way that forgets the fuzziness of sets and maps, and formalizing the inclusion functor ip.

Set → CF-Set.

In addition, we study of the applications of universal arrows in category F-Set, and getting back to the classical state and comparing it with that introduced in [10].