Abstract:

Based on the concept of the F-rough integral proposed by Yu［1］, 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-rough integral was discussed. It was proved that the β-rough integral is a generalization of the F-rough integral, while the F-rough integral is a special case of the β-rough integral.

Key words: function one direction S-rough sets; F-rough integral; transfer credibility degree β; β-rough integral