基于偏好不一致熵的有序决策

针对多规则有序决策系统中的偏好决策问题，根据有序决策的偏好不一致特性，提出了一种基于偏好不一致熵的偏好决策方法。首先，定义了样本的偏好不一致熵（PIEO），用来度量特定样本相对于样本集的偏好不一致程度；然后，根据偏好决策中不同属性对决策的重要性不同的特点，提出了一种加权的样本偏好不一致熵，并结合属性偏好不一致熵在度量属性重要性方面的能力，给出了一种基于属性偏好不一致熵的权值的计算方法；最后，提出了一种基于样本偏好不一致熵的偏好决策算法。采用Pasture Production和Squalsh两个数据集进行仿真实验，基于全局偏好不一致熵分类后，各属性的偏好不一致熵普遍比基于向上和向下偏好不一致熵分类后的熵值小，而且更接近原始决策的偏好不一致熵，这说明基于全局偏好不一致熵的分类比其他两种情况的分类效果好。分类偏离度最小低至0.1282，这说明分类的结果比较接近原始决策。

Ordered decision-making based on preference inconsistence-based entropy

Aiming at the problem of preference decision in multi-rule ordered decision-making system, according to the preference inconsistency of ordered decision-making, a preference decision-making method based on preference inconsistent entropy was proposed. Firstly, the Preference Inconsistence Entropy of Object (PIEO) was defined and used to measure the degree of preference inconsistency for a particular sample relative to the sample set. Then, according to that different attributes have different importances to the preference decision, a weighted Preference Inconsistence-based Entropy of Object (wPIEO) was proposed. Moreover, combining wPIEO with attribute preference inconsistency entropy in measuring attribute importance, a weighting method based on attribute preference inconsistent entropy was proposed. Finally, a preference decision algorithm based on sample preference inconsistent entropy was proposed. Two data sets, Pasture Production and Squalsh, were used to simulate the experiment. After the global Preference Inconsistent Entropy (gPIE) classification, the preference inconsistent entropy of each attribute was generally smaller than the entropy value based on the preference inconsistent entropy classification based on the up and down preferences, and it was closer to the preference inconsistent entropy of the original decision, which indicates that the classification based on gPIE was better than the other two cases. The classification deviation was as low as 0.1282, indicating that the classification results are close to the original decision.