基于一般二元关系的粗糙集加权不确定性度量

A Weighted Uncertainty Measure of Rough Sets Based on General Binary Relation

不确定性度量是粗集理论的研究热点.考虑到实际数据中样本重要性的不同,在一般二元关系下构建一种带有可调参数的加权不确定性度量———α熵,证明了现有的多种不确定性度量是α熵的特例,进而对完备和不完备信息系统中知识的不确定性度量进行了统一.在此基础上基于一般二元关系提出了一种加权不确定性度量———α精度和α粗糙度,证明了α精度和α粗糙度的单调性;理论分析和实例表明α精度和α粗糙度比现有的不确定性度量更精确,更符合人们的认识规律.最后,在一般二元关系下利用α精度设计了一种加权属性约简算法,实验结果表明文中的变参数加权不确定性度量方便地融入了主观偏好和先验知识,通过改变参数α构造的组合分类器有效地提高了约简结果的分类精度.这些结论发展了基于粗糙集的不确定测度理论,提高了方法的普适性和可解释性,为一般二元关系下的信息系统知识获取提供了理论依据.

Uncertainty measure is one of the important aspects of rough set theory. A new kind of weighted uncertainty measure called a-entropy is presented under general binary relation by considering the sample data with different importance, and some existing uncertainty measures are a special case of a-entropy by adjusting the variable parameter a. Thus it unites the corre- sponding uncertainty measures of complete and incomplete information systems. In addition, a well-justified uncertainty measures, a-roughness （a-accuracy） is proposed based on a-entropy. It is proved that a-roughness （a-accuracy） decreases （increases） monotonously as the information granularities become smaller. The numerical example proves that the a-accuracy and a-roughness are more reasonable and accurate than the existing methods. Finally, under general binary relation, a new heuristic weighted attribute reduction algorithm is proposed based on a-accuracy. The experiments demonstrate that the weighted measures in this paper provide a method for combining the subjective preferences and prior knowledge in uncertainty measures, and the combina- tion classifier based on the variable parameter a can improve the accuracy of classification. These investigations developed the uncertainty theory and provide theory basis for knowledge acquisition in information systems based on general binary relation.