基于多特定决策类的不完备决策系统正域约简

现有的属性约简方法大部分关注决策系统中的所有决策类,而在实际决策过程中决策者往往仅关注决策系统中的一种或几种决策类。针对上述问题,提出基于多特定决策类的不完备决策系统正域约简的理论框架。首先,给出不完备决策系统单特定决策类正域约简的概念;第二,将单特定决策类正域约简推广到多特定决策类,构造了相应的差别矩阵及区分函数;第三,分析并证明了相关定理,提出基于差别矩阵的不完备决策系统多特定决策类正域约简算法(PRMDM);最后,选取4组UCI数据集进行实验。在数据集Teaching-assistant-evaluation、House、Connectionist-bench和Cardiotocography上,基于差别矩阵的不完备决策系正域约简算法(PRDM)的平均约简长度分别为4.00、13.00、9.00和20.00,PRMDM算法(多特定决策类中决策类数目为2)的平均约简长度分别为3.00、8.00、8.00和18.00。实验结果验证了PRMDM算法的有效性。

Positive region preservation reduction based on multi-specific decision classes in incomplete decision systems

The existing attribute reduction algorithms mostly focus on all decision classes in decision systems, but in actual decision process, decision makers may only focus on one or several decision classes in the decision systems. To solve this problem, a theoretical framework of positive region preservation reduction based on multi-specific decision classes in incomplete decision systems was proposed. Firstly, the positive region preservation reduction for single specific decision class in incomplete decision systems was defined. Secondly, the positive region preservation reduction for single specific decision class was extended to multi-specific decision classes, and the corresponding discernibility matrix and function were constructed. Thirdly, with related theorems analyzed and proved, an algorithm of Positive region preservation Reduction for Multi-specific decision classes reduction based on Discernibility Matrix in incomplete decision systems (PRMDM) was proposed. Finally, four UCI datasets were selected for experiments. On Teaching-assistant-evaluation, House, Connectionist-bench and Cardiotocography dataset, the average reduction length of Positive region preservation Reduction based on Discernibility Matrix in incomplete decision systems (PRDM) algorithm is 4.00, 13.00, 9.00 and 20.00 respectively while that of the PRMDM algorithm (with decision classes in the multi-specific decision classes is 2) is 3.00, 8.00, 8.00 and 18.00 respectively. The validity of PRMDM algorithm is verified by experimental results.