Algorithms for Different Approximations in Incomplete Information Systems with Maximal Compatible Classes as Primitive Granules

This paper proposes some expanded rough set models with maximal compatible classes as primitive granules, introduces two new granules for extending rough set model, and designs algorithms to solve maximal compatible classes, to find the lower and upper approximations according to the newly granules, to compute reducts and minimal reducts with attribute significance. It also verifies the validity of algorithms by examples. These provide an important and implemental theoretical base for rough set theory to deal with problems in incomplete information systems.