关键词: 条件信息熵,正区域,代数约简,算法 中图法分类号TP18文献标识码A

Abstract: A semantic analysis on how to keep positive region unchanged was given．An improved conditional information entropy was proposed．It was proved that remaining the modified conditional information entropy unchanged and remaining positive region unchanged are equivalent．Therefore,some main concepts of algebraic reduction were described by the revised conditional information entropy．However,a counter example illustrates that its monotonicity does not hold,which means a heuristic reduction algorithm can not be constructed based on bottom-up．Any attribute in an algebraic consistent set is not irreversible if it is checked unsuppressible．An efficient algorithm based on top-down was proposed,which starts from condition attribute set,removes the unnecessary attribute step by step．It is finally guaranteed to obtain an algebraic reduction by traversing the attributes only once．Numerical example and the experimental results show that the algorithm is valid and efficient.

Key words: Conditional information entropy,Positive region,Algebraic reduction,Algorithm