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Bayesian Theorem In Rough Set Background And Its Application To Recovering Image

Bayesian theorem is widely used in the fields of machine learning and computer vision. But the classic Bayesian theorem only focuses on the situations with a finite or countable partition of sample space, which sets a limitation on its applications. This paper first generalizes it by means of conditional mathematical expectation, and proceeds to propose a conjecture about it. Second, this paper introduces the concept of rough lower probability in approximation space; thereafter, the multiplication rule, the law of total probability and Bayesian theorem in classic probability are generalized into the rough background. Thirdly, the application of the generalized Bayesian theorem into the computer is suggested.