Abstract
The generalized information systems contain complete information systems, incomplete information systems and multivalued information systems. Some concepts and properties of rough sets based on generalized information systems are given in this paper. We extend the rough set theory to the generalized information systems. We also discuss the describing forms of decision of the generalized information decision system and propose some definitions and properties of the certain rules and optimal certain rules. It is easy to transform the describing forms of decision of the generalized information decision system into the Skolem's standard form and apply it directly to resolution inference in artificial intelligence.
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