Research On Granulation Reduction Algorithm For Multi-granulation Rough Set

Rough set theory is a mathematical tool proposed by the Poland scholar Z.Pawlak in 1982,which can effectively deal with inaccurate and uncertain information.The classical rough set model takes complete information system as the research object,based on the equivalence relation,and divides the domain with one attribute group.From the point of view of granular computing,the classical rough set model is based on single granularity and single level,and can not analyze and deal with problems from multi-granulation and multi-level.In order to make the rough set can better solve practical problems,The multi-granulation rough set model is proposed by Qian,in multi-granulation rough set,decision making can be characterized by information particle of multiple granularity spaces,so it can analyze the problem from multi-angle and multi-level so as to obtain more satisfactory and reasonable the result Since the multi-granulation rough set model is proposed,researchers have proposed many extended models and granulation reduction algorithms for multi-granulation rough set.However,the presented granulation reduction algoritithms for multi-granulation rough set is mainly based on complete information system and the efficiency of the algorithm is low.In order to solve these problems,this paper takes the multi-granulation rough set as the research background and carries out the following research.(1)In order to improve the efficiency of granulation reduction for multi-granulation rough set,a granulation reduction algorithms for multi-granulation rough set based on matrix is proposed.Firstly,taking decision information system as the object,in order to simplify the calculation of lower approximation of decision class in the process of granulation reduction,the definition of positive domain matrix under multiple granularities of decision information system is given,in order to facilitate the granularity selection in the process of granulation reduction,the definition of column matrix of granularity is given.Then,based on the matrix calculation,the calculation method of important measure of granularity is redefined and proving that the new calculation method of important measure of granularity is equivalent to the classical,and then a granulation reduction algorithm of multi-granulation rough set based on matrix is proposed with the important measure of granularity as heuristic information.Finally,the effectiveness and efficiency of the proposed algorithm are verified by the experiment on the open data set.(2)A granulation reduction algorithm based on granularity mixed importance is proposed for incomplete information system.Firstly,the data loss rate on granularity is introduced,and the mixed important measure of the granularity is defined by combining the important measure of the granularity with data loss rate on granularity.Then,a granulation reduction algorithm for incomplete systems is designed with the mixed important measure of the granularity as the heuristic function,an example is given to analyze the advantages of the algorithm.Finally,the experiment verified the effectiveness of the proposed algorithm,by adjusting the parameters,the algorithm can obtain the results of granulation reduction for different needs.