决策细化的粗糙集理论分析

Analysis of Rough Set Theory on Decision Subdivision

对基于粗糙集的决策系统,从理论上分析了决策数据细化的程度对规则近似质量、近似分类精度、核属性和信息熵的影响.证明了决策属性的属性值划分越细,则其规则近似质量、近似分类精度和信息熵就越小,并且决策表中决策属性值细化后所得到的核属性集一定包含细化前的核属性集.因此,在对决策属性离散化时,决策数据细化的程度要适宜.研究结果对研究决策表属性的约简、决策规则的形成和有效性等问题具有实际意义.

The degree of subdivision of the decision attribute value directly influences upon the approximation quality of rules, accuracy of approximation classification, core attributes and information entropy in decision systems based on rough set theory. It is theoretically demonstrated that the finer the decision attribute discretization of a decision table is, the lower the approximation quality of rules, and the accuracy of approximation classification and information entropy are on any attribute set. Meanwhile, if the attribute values of decision attributes are divided into finer values, then the core attributes set obtained from the finer decision table must include the core attributes set obtained from the previous decision table. So the refinement degree of decision data should be chosen properly in the discretization of decision attributes. The research is helpful for the attribute reduction, formation of decision rules and enhancing confidences of decision rules.