Abstract: Pawlak proposed the rough set model, in order to processing data and knowledge which are imprecise or uncertainty in artificial intelligence. Then, the rough set model has been extended and many new rough set models have been put forward. Inhere are two main methods of extension, one method is to weaken the dependence of equivalence relation, the other is to expand the domain from one to two, and Y. Y. Yao ever proposed a rough set model of two-do-main. In this paper, we made some research for Cartesian product rough models based on two(finite) approximation spaces, and gave the concept of product approximation space. Afterwards, we described the upper(lower) approximation of decomposable subsets of a Cartesian product, and the approximate precision and roughness of decomposable subsets.Finally, we studied the decomposable problem of Cartesian product rough models, and obtained the sufficient and necessary conditions of decomposition of a product approximation space.

Key words: Cartesian product, Product approximation space, Decomposable sunset, Roughness, Decomposable approximation space