In this paper, we have described with certain detail some theories of the fuzzy logic, and their application to the artificial intelligence like scheme of representation of the knowledge, like base of new reasoning models, and also like effective means of approaching the problem of the linguistic classification of variables. After a fleeting representation of the nature and reach of the fuzzy sets, we enter of full in their characterization and nomenclature. Subsequently we approach the problems of the fuzzy relationships, and we propose the formulation of Zadeh for the representation of knowledge of the type: If x is A, Then y is B. This allows us to define the generalized modus ponens as inferential mechanism of the fuzzy systems. Finally, it is mentioned some of the reasoning ways that can be found in the fuzzy systems.