中文摘要：

基于文献提出的F-粗积分概念，引入迁移信度卢，提出在迁移信度β条件下的-β粗积分，讨论F-粗积分与β粗积分的关系，证明β-粗积分是F-粗积分的推广，F-粗积分是β粗积分的特例。

英文摘要：

Based on the concept of the F-rough integral proposed by Yu , the concept of the β-rough integral was given by employing the transfer credibility degree β, the relation between the F-rough integral and the β-mugh integral was discussed. It was proved that the β-mugh integral is a generalization of the F-rough integral, while the F-rough integral is a special case of the β- rough integral.