The Research And Application On Quotient Space Combination

The framework of quotient space theory is proposed by the domestic scholars Academician Zhang Bo and Professor Zhang Ling in the1980s, which has become one of the three models of granular computing. In quotient space theory, triplet (X,T,f) is proposed to describe a problem space, where X denotes the universe; T is the structure of universe X, namely the relationship of different items at universe X; and f:xâ†'y indicates the attributes of universe X. The resolving problem (X,T,f) is the process of analyzing and researching the universe X,the attributes f and the structure T. The research of quotient space theory consist of three aspects, including combination, reasoning and projection.This combination studies the relationship between the quotient space and the original space, which is the basis of the quotient space theory. In this thesis, we expand the universe combination and structure combination and provide some useful property about combination of quotient space, in order to describe the relationship between the original space and quotient space more clearly. In the meanwhile, we analyze the combination of attribute function and gives a example. At present the combination method do not discuss and describe the relationship between the quotient space and quotient space, so in this thesis, we use fuzzy equivalent relation indicate the different perspectives and different level of quotient space. Then we extend the combination method of quotient space to the combination of multiple perspectives and give a combination model.Research question from the perspective of multi-granularity conforms to human cognitive characteristic, in this paper, we apply the combination method of quotient space to the FCM clustering algorithm. Firstly, we do combination operation for before and after in the process of FCM algorithm iteration,using the result of synthesis to update the cluster center, which can guarantee the stability of clustering processing. Secondly, we analyze the granularity theory of FCM algorithm and provide a new objective function which is base on granularity theory This objective function can effectively reduce the number of iterations in the process of clustering.