属性细化的粗糙集理论分析

针对粗糙集的决策系统,给出了有效等价类细化和有效集合细化的定义,从理论上分析了必要属性细化后对上近似和下近似、近似分类精度和质量以及决策规则的数量和相对约简的影响.针对细化的区域分三种情况讨论,得出了在各种区域下划分的结果,如果对有效集合细化划分的越细,上近似和下近似就越逼近给定的集合,分类精度和近似分类质量就越大,产生的规则在包含原规则的基础上增多,并且相对约简和属性的必要和不必要的性质保持不变.研究结果对决策表的属性约简、决策规则形成和有效性等问题具有实际意义.

Analysis of Rough Set Theory on Attribute Subdivision

The definitions of effectively equivalent class subdivision and effective set subdivision are given to the decision system by rough set theory. The influence of the necessary attributes after class subdivision on the upper and lower approximate values, quality and accuracy of approximate classification, number of decision-making rules and relative reduction are analyzed theoretically. Three cases concerning different subdivision regions are discussed with relevant results obtained. It is theoretically revealed that the finer the effective set subdivided, the closer the lower and upper approximate values to the original set and the higher the quality and accuracy of approximate classification and, at the same time, the more the number of the decision-making rules increased. In addition, the relative reduction and the necessity and unnecessity of attributes all remain unchanged. The results revealed provide an actual significance to the attribute reduction, formation of decision-making rules and their effectiveness.