Abstract: In view of the fact that the uncertainty measures of classical rough set theory are difficult to be suitable for neighborhood rough set model, this paper proposes an uncertainty measurement method based on information  entropy and neighborhood rough sets. By the definitions of neighborhood relation, each object in the universe is    assigned with a neighborhood subset, called neighborhood granule. Some uncertainty measures of neighborhood granule are defined, including approximate accuracy, information entropy and weighted information entropy in the neighborhood system. Furthermore, this paper presents the axiomatic concept of measure, and proves that the three measures are axiomatic uncertainty measures. This paper also gives the maximum and minimum of these measures and proves their monotonicities. Theoretical analysis and experiments show that the information entropy measure in the neighborhood system is better than the approximate accuracy measure.

Key words: neighborhood rough sets, neighborhood information entropy, uncertainty measure, information system, approximation accuracy

摘要： 针对传统粗糙集理论中不确定度量方法难以适用于邻域粗糙集模型的问题，引入信息熵的度量方法，提出了基于信息熵的邻域粗糙集不确定性度量方法。该方法采用邻域关系对连续型数据进行信息粒化，基于粒化后的数据定义邻域系统中的近似精度、邻域信息熵、加权邻域信息熵等不确定性度量。进一步提出邻域系统不确定性度量的公理化表示，证明邻域系统的近似精度、邻域信息熵、加权邻域信息熵都是公理化度量；给出其最大最小值，证明其满足单调性原理。理论分析与实验表明邻域系统中的信息熵度量优于近似精度度量。

关键词: 邻域粗糙集, 邻域信息熵, 不确定性度量, 信息系统, 近似精度