关键词: 粗糙集, 优势关系, 广义决策约简, 上近似约简, 辨识矩阵

Abstract: Generalized decision reduction and upper approximation reduction based on dominance relation have been defined. It is proved that a generalized decison reduction based on dominance relation is equivalence to upper approximation reduction based on dominance relation. The judgement theorems and discernibility matrixes with respect to generalized decision reduction and upper approximation reduction based on dominance relation are established, from which we can obtain algorithms for finding generalized decision reduction and upper approximation reduction based on dominance relation. Compared with the algorithm for finding a discernibility matrix with respect to upper approximation reduction, the time complexity of the algorithm for finding a discernibility matrix with respect to generalization decision reduction is lower. So the discernibility matrix with respect to generalization decision reduction can be used to find upper approximation reducts and generalized decision reducts.

Key words: Rough sets, Dominance relation, Generalized decision reduction, Upper approximation reduction, Discernibility matrixes