摘要
更低的近似积分，上面的近似积分和不平的积分的概念根据功能被给不平的集合。把概念，更低的近似积分的关系，上面的近似积分的关系，不平的积分的关系，和不平的积分的双中部的定理基于这些被讨论。不平的积分有有限收缩特征和有限延期特征。
The concepts of the lower approximation integral,the upper approximation integral and rough integrals are given on the basis of function rough sets.Based on these concepts,the relation of the lower approximation integrals,the relation of the upper approximation integrals,the relation of rough integrals,and the double median theorem of rough integrals are discussed.Rough integrals have finite contraction characteristic and finite extension characteristic.
基金
Supported by the Natural Science Foundation of Shandong Province（ZR2010AL019）
Supported by the Education Science Foundation of Shandong Province（2010JZ123）
关键词
工作不平的集合
更低的近似积分
上面的近似积分
不平的积分
function rough sets
the lower approximation integral
the upper approximation integral
rough integrals
