广义多尺度决策系统中基于可变精度的最优尺度组合

针对广义多尺度决策系统的知识表示与知识获取问题,讨论广义多尺度决策系统中基于对偶概率粗糙集模型的最优尺度组合选择问题.定义广义多尺度决策系统中β下近似最优尺度组合、 β上近似最优尺度组合、 β信任分布最优尺度组合与β似然分布最优尺度组合概念,分析不同最优尺度组合之间的关系与特征,证明当β在特殊的阈值范围内时, β下近似最优尺度组合与最大分布最优尺度组合等价,而β上近似最优尺度组合与广义决策最优尺度组合等价.

Variable Precision Based Optimal Scale Combinations in Generalized Multi-scale Decision Systems

To solve the problems of knowledge representation and knowledge acquisition in generalized multi-scale decision systems, optimal scale combination selections based on dual probabilistic rough set model in generalized multi-scale decision systems are discussed. Notions of β lower approximation optimal scale combination, β upper approximation optimal scale combination, β belief distribution optimal scale combination and β plausibility distribution optimal scale combination in generalized multi-scale decision systems are defined and their properties are examined. Finally, relationships among different notions of optimal scale combinations in generalized multi-scale decision systems are analyzed. It is proved that for some special thresholds, β lower approximation optimal scale combination is equivalent to the maximum distribution optimal scale combination, whereas β upper approximation optimal scale combination is equivalent to the generalized decision optimal scale combination.