This paper points out that the limit theory,without distinction of different infinity,covers unstrictness of classical calculus; and that, on the basis of the study of the fuzzy property of infinity, it is necessary to introduce fuzzy cardinality.

An on-line tracking self-learning algorithm for fuzzy basis function(FBF)neural network classi- fier is proposed in this paper.

Most of the existing intelligent fault diagnosis systems are lack of the ability to track the operation behavior of the machine,thus a online tracking self-learning algorithm for the fuzzy basis function(FBF) network was researched,which was used in the behavior-based intelligent fault diagnosis system.

The support vectors which are used for confirming the fuzzy basis function and creating the corresponding fuzzy rules were extracted from the training samples by the learning mechanism of SVM, and the fuzzy reasoning model was build up as a result.

A fuzzy direct adaptive control is designed for GDROV motion control by using fuzzy basic functions to approximate the optimal control output and by adjusting the adaptive law with fuzzy logic dynamically.

A versatile fuzzy sliding-model adaptive controller with a bank of general rules is being presented on the basis of a newly derived self-learning algorithm, in combination with fuzzy based functions of a fuzzy logic system.

Universal optimization for adjustable parameters of fuzzy based function is realized by using GA and finding adjust law of parameters in general designing adaptive controller is replaced.