多尺度决策系统中高效下近似跳转算法研究

Research on Efficient Lower Approximation Transition Algorithm Based on Multi-Scale Decision Systems

摘要: 经典粗糙集理论只能从单个尺度处理分析数据，多尺度决策系统则可以从粗细不同尺度深度挖掘数据中隐含的信息，该系统的提出拓宽了经典粗糙集的应用范围，成为粗糙集领域的重要研究方向之一，受到学者广泛关注。由于传统方法下各尺度间下近似的转换仍需要消耗较多资源，因此本文提出一种下近似快速跳转方法。在基于乐观多粒度的多尺度决策系统的背景下，利用多尺度决策系统中特有的粒度转换函数实现了尺度由细向粗跳转时下近似的快速更新，并提出了相应的更新算法，有效避免了重新对数据表的遍历。为了验证算法的有效性，实验使用9个UCI数据集从下近似结果及时间方面分别进行验证，结果表明本文所提出的算法可行且具有更高的效率。

Abstract: Classical rough set theory can only process and analyze data from a single scale, whereas a multi-scale decision system can deeply mine the information hidden in the data from different coarse and fine scales. The introduction of multi-scale decision systems has expanded the application scope of classical rough set theory, establishing it as a significant research direction within the field and garnering widespread attention. However, traditional methods for transitioning lower approximations across scales still consume considerable resources. To address this, this paper proposes a rapid transition method for lower approximations. Initially, the multi-scale decision system is integrated with optimistic multigranulation rough sets. Building on this foundation, the method leverages the granular transformation functions of multi-scale decision systems to facilitate swift updates of lower approximations during scale transitions from fine to coarse. This approach introduces a fast update algorithm for lower approximations as scales coarsen, effectively circumventing the need for repeated traversal of data tables. To validate the algorithm’s efficacy, experiments were conducted using nine UCI datasets, assessing both the results of lower approximations and computational time. The findings demonstrate that the proposed algorithm is not only feasible but also exhibits superior efficiency.