自反二元关系下不完备信息系统的粗糙熵及粒度度量

针对不完备信息系统中各种自反二元关系形成了对系统的覆盖而非划分的情况,提出利用对象的邻域来定义粗糙熵和粒度度量以衡量系统的不确定性,证明了以上不确定性度量同完备信息系统的不确定性度量是一致的.同时在覆盖可约简的情况下,定义了覆盖约简对系统的粗糙熵和粒度度量,研究结果表明在系统分类最细或最粗时,覆盖约简的不确定性和知识的不确定性是等价的.

Rough Entropy and Granularity Measure to Incomplete Information System Under the Reflexive Binary Relation

The reflexive binary relations constitute coverage not a partition to the incomplete information system.Based on this situation,the definition of rough entropy and granularity measure using the neighborhood of object is proposed to measure the uncertainty of information system,and it is proved that the definitions are consistent with the uncertainty measurement of complete information system.Considering the redundancy of the coverage to system,the rough entropy and granularity measure of coverage reduction to the incomplete information system is also defined,meanwhile,research results show that the uncertainty of coverage reduction is equivalence to that of knowledge when the classification of system reaches to an extreme value.