Rough controllers with state feedback
Engineering Applications of Artificial Intelligence
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Knowledge reduction is one of the most important tasks in rough set theory, and most types of reductions in this area are based on complete information systems. Though one of the extended relations, similarity relation, has been pre- sented in incomplete information systems, which do exist in real world, its reduction approach has not been examined. In this paper, based on similarity relation, the upper and lower approximation reduction are defined in incomplete information systems. The judgment theorems with respect to the consistent sets of the upper and lower approxima- tion reduction are studied, their discernibility matrices are obtained and the approaches of the upper and lower ap- proximation reduction based on discernibility matrices are presented. To overcome its drawback of NP-hard time com- plexity, two heuristic algorithms based on significance of attributes are proposed.