不协调覆盖决策系统的完备属性约简算法

A Complete Attribute Reduction Algorithm for Inconsistent Covering Decision Systems

属性约简是不协调覆盖决策系统中的核心问题之一。该文在不协调覆盖决策系统中提出了具有非负性和单调性的限制信息熵、限制条件信息熵与限制互信息,在此基础上讨论了协调集、约简以及核的等价判定定理;然后,在不协调覆盖决策系统中提出了一种完备的具有多项式时间复杂度的启发式属性约简算法,并通过评估房屋出售情况的例子说明该算法的可行性与有效性。

Attribute reduction is one of the key issues in inconsistent covering deeision systems. In this paper, new limitary information entropy, limitary conditional information entropy and limitary mutual information are defined in inconsistent covering decision systems and are proved to be both nonnegative and monotonous. Then, from the perspective of information theory the necessary and sufficient conditions of a consistent set, a reduct and the core of an inconsistent covering decision system are presented. Furthermore, a heuristic attribute reduction algorithm with polynomial time complexity is proposed for inconsistent covering decision systems and it is proved to be complete. Finally, a real example of evaluating houses is employed to demonstrate both feasibility and effectiveness of the proposed algorithm.