基于边界域条件熵的不确定性度量标准

不确定性度量研究是粗糙集理论的重要问题之一，系统的不确定性是由边界域的存在造成的。根据变精度粗糙集思想，将边界域对象分成弱一致性对象和不一致对象集合。结合信息熵与不确定性间的关系，提出一种基于边界域条件熵的不确定性度量标准。通过理论分析证明，边界域条件熵在衡量决策系统一致性程度时，与普通条件熵具有相同的判别作用；在粗糙集特征约简的启发式条件中与粗糙集正域等效。

Uncertainty measure criterion based on conditional entropy of boundary region

The research of uncertainty measure is the key point of the rough sets’ theory. The uncertainty of decision information system is produced by boundary region. Based on the theory of variable precision rough sets, the objects of boundary region are divided into weak-consistent objects and inconsistent objects. This paper builds an uncertainty measure criterion on conditional entropy of boundary region. Theoretical analysis proves that in case of weighing the consistency of decision system, this conditional entropy of boundary region have something in common on recognition with the normal conditional entropy, and this measure criterion is also equivalent to the relative regular domain in feature reduction of rough sets.