Optimal Approximation And Reduction Of Incomplete Information Systems Based On Maximal Consistent Block

Rough set theory,as a mathematical tool that can effectively analyze and process imprecise,incomplete and inconsistent information,has been widely used in various fields in recent years.If the similarity degree between the upper and lower approximation of the rough set and the target set is not very large,the accuracy of rule extraction will be not high and the uncertainty will be large.To solve this problem,this paper studies the algorithm of optimal approximation and reduction in incomplete information systems.The contents are as follows:In incomplete information systems,according to the approximate problem,the optimal approximation of the heuristic algorithm is presented.The optimal approximation is the definable set with the maximum similarity degree with the target set,and it is located between the upper and lower approximation.Therefore,in this paper,the knowledge granularity of boundary region are gradually added to the lower approximation(or gradually removed from the upper approximation),until reaches the maximum similarity degree,thus obtains the optimal approximation,and the heuristic algorithm for the optimal approximation in incomplete information systems is designed by using the maximal consistent block.Examples show that the algorithm is effective.In incomplete decision systems,two reduction algorithms are proposed for attribute reduction.Firstly,a heuristic algorithm for the reduction of the optimal approximate similarity distribution is designed based on the heuristic information of attribute importance.Secondly,on the basis of the maximal consistent block,the discernibility matrix is constructed with the optimal approximation,and an algorithm for the optimal approximation reduction of the incomplete decision systems is designed.Finally,examples show that the two algorithms are effective.