关键词: 粗集，空值，等价关系，集对分析，不完备信息系统

Abstract: In view of the limitations of existing extension of rough set models for processing incomplete information, the difference between null value's ectuality and known value's equality was analysed on probability. Based on the theory of Set Pair Analysis, SPA Similarity Degree and Similarity I}olerance Relation were proposed, and the method of extension of rough set model based on SPA Similarity Degree was described also. It discriminates null value’s equality from known value's equality by using the coefficient of difference degree,and gets the neighborhood of object according to coefficient of difference degree and similarity tolerance relation, than gets upper approximation and lower approximation according to the neighborhood. The difference of null value's equality is ignored when we compute upper approximalion, and the difference of null value's equality is emphasized for lower approximation. The results of the experiment reveal that both the classification capability and the precision of rough set arc better than other models.

Key words: Rough set, Null value, Equivalence relation, Set pair analysis, Incomplete information system