Fuzzy Sets Category and Applications of Its Universal Arrows

This paper introduces a generalization of the concept of Set category introduced in [10] by constructing the category - whose objects are small ℒ - fuzzy sets in which the characteristic functions takes its values from a complete distributive lattice, and its arrows are ℒ - fuzzy maps. After that we construct a functor - between these two categories, in a way that forgets the fuzziness of sets and maps, and formalizing the inclusion functor - . In addition, we study of the applications of universal arrows in category - , and getting back to the classical state and comparing it with that introduced in [10].

On Upper Fuzzy Prime Ideal over Rings

In this paper we shall study the definition of upper fuzzy prime ideals, Tupper fuzzy prime ideals and T-S- upper weakly fuzzy prime ideals proving the inclusion relationships that are satisfied among them. Examples are given showing that some relationships don’t hold between these types of ideals. On the other hand we use these definitions to study some properties, proposition and theorems.

The Upper Fuzzy Index

In this paper we shall study the upper fuzzy index with the upper fuzzy subgroups, also we shall give some new definitions for this subject. On the other hand we shall give the definition of the upper normal fuzzy subgroups, and study the main theorem for this. We shall also give new results on this subject.