Classifier Research

It is always necessary to distinguish and classify things when understanding and transforming the nature. With the rapid development of science and technology, this distinction and classification of things appear in more and more human activities. In the course of classification and differentiation, researches have grasped some characteristics or observations, which on the one hand separate some things, one the other hand, merge them. In the paper, we called it asymmetric separator, which is a binary relation on discourse domain, and cannot separate the same elements. If it can separate the two elements A and B, it can separate A and C or B and C, for any element of C.The distinction and classification of things cannot do without its distance. Asymmetric distance, which plays an important role in the research of nonlinear systems and algorithm, is a promotion of the distance. This article describes some basic concepts such as non-symmetric metric space, asymmetric norm space and quasi-uniform structure, and gives relevant results.This paper proposes the concepts of asymmetric separator and a method for asymmetric separator unclear of general binary relation. Researching the asymmetric set separator produced by set, asymmetric set of family separator produced by set of family, and asymmetric function separator produced by function. We established the asymmetric metric space induced by asymmetric separator, which uses the number of asymmetric separator (can separate their asymmetric separator in the number or measure) to determine the asymmetric separator, in the set of asymmetric separator space. Then by extending the asymmetric separator space to asymmetric separator structure, we draw the conclusion that any asymmetric metric are asymmetric separator structure.This paper promotes the concept of asymmetric separator to fuzzy asymmetric separator. With the corresponding, it has the fuzzy asymmetric set separator produced by fuzzy set, fuzzy asymmetric set of family separator produced by fuzzy set of family, and fuzzy asymmetric function separator produced by fuzzy function. At last, the paper discusses the asymmetric separator polynomial, and then proposes the small element method of asymmetric separator reduction, and the reduction algorithm of asymmetric separator.The concept of asymmetric separator also can be extended to random asymmetric and sequence asymmetric separator, which is the prospect of future study.