This paper define the efficient combination and efficient combine function,study the periodic of efficient combine function derivative and indefinite integral of efficient combine function.

The advantage of this algorithm is that only making the matrix multiplication operation or solving equations set, can the decending direction of minimax be obtained without having need to consider how many effective functions there are and how to calculate the inverse matrix.

In this paper the entropy preservability of S-Box is discussed and the definitions of condition entropy and entropy preservability of nonlinear S-Box and combining function are presented.

In this paper,by using the Subtractive Clustering Method and clustering validity function,set up the clustering center point was and the clustering classes in this new method,auto-adapted clustered the data set was implemented,and applied this method to the segmentation for CT images.

This article aim at failing of convergence rate is too slow in the based on common FCM arithmetic and validity function arithmetic,because it use Gauss randomicity to update dimensions powers,use genetics to accelerate convergence rate.

The optimal feature number is decided automatically by the introduced cluster validity function.

Validity measure function is introduced to the kernel clustering algorithm, and it can get the sorts’ number automatically.

Kernel function and validity measure function are introduced to the fuzzy clustering algorithm, and fuzzy kernel clustering self-adaptive algorithm is proposed.