划分序乘积空间约简算法研究

徐怡, 陶强

系统工程理论与实践 ›› 2025, Vol. 45 ›› Issue (2) : 554-570.

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中国科学院数学与系统科学研究院期刊网
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系统工程理论与实践 ›› 2025, Vol. 45 ›› Issue (2) : 554-570. DOI: 10.12011/SETP2023-2131
论文

划分序乘积空间约简算法研究

    徐怡1,2, 陶强1
作者信息 +

Research on the reduction algorithm under partition order product space

    XU Yi1,2, TAO Qiang1
Author information +
文章历史 +

摘要

多视角和多层次是粒计算(granular computing)中问题求解的两个基本原则. 划分序乘积空间作为一种新的粒计算模型, 遵循多视角和多层次的原则, 能够从多个视角和多个层次来描述和解决问题. 但是划分序乘积空间是一种格结构, 在划分序乘积空间中寻找合适的问题求解层通常是一个NP难问题, 特别是当视角和层次存在冗余时, 会导致划分序乘积空间结构庞大且复杂. 因此通过对视角和层次的约简, 可以有效降低划分序乘积空间的复杂性. 现有的度量指标, 例如决策支持度、 条件熵、 最大包含度和距离度量等, 不能有效地对视角、 层次和属性进行约简, 本文在划分序乘积空间中将距离度量、 最大包含度和最大决策的概念相结合, 引入了一种新的基于距离度量最大包含熵的单调不确定性度量标准. 在此基础上, 分别定义了视角重要度、 层次重要度与属性重要度, 并且分别给出了视角、 层次和属性的约简算法, 可以对多个视角进行约简、 多个视角中的多个层次进行约简和对每个层次中的属性进行约简, 有效降低了划分序乘积空间下的复杂度. 实验结果证明了, 所提约简算法的有效性.

Abstract

Multi-view and multi-level are the two basic principles of problem solving in granular computing. Partition order product space as a new granular computing model follows the principle of multi-view and multi-level, which can describe and solve problems from multi-view and multi-level. However, partition order product space is a lattice structure, and finding a suitable problem solving layer in partition order product space is usually an NP difficult problem, especially when there is redundancy in views and levels, which will lead to the large and complex structure of partition order product space. Therefore, by reducing the views and levels, the complexity of partition order product space can be effectively reduced. Existing metrics, such as decision support, conditional entropy, maximum inclusion and distance measurement, cannot effectively reduce the views, levels and attributes, and this paper combines the concepts of distance measurement, maximum inclusion and maximum decision in the partition order product space, and introduces a new monotonic uncertainty metric based on distance measurement of maximum inclusion entropy. On this basis, the importance of view and level importance are defined respectively, and the reduction algorithms of view and level are given respectively, which can reduce multi-views and multi-levels under each view, which effectively reduces the complexity under the partition order product space. Experimental results prove the effectiveness of the proposed reduction algorithm.

关键词

多视角 / 多层次 / 视角约简 / 层次约简 / 属性约简 / 划分序乘积空间 / 距离度量

Key words

multi-view / multi-level / view reduction / level reduction / attribute reduction / partition order product space / distance measurement

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导出引用
徐怡 , 陶强. 划分序乘积空间约简算法研究. 系统工程理论与实践, 2025, 45(2): 554-570 https://doi.org/10.12011/SETP2023-2131
XU Yi , TAO Qiang. Research on the reduction algorithm under partition order product space. Systems Engineering - Theory & Practice, 2025, 45(2): 554-570 https://doi.org/10.12011/SETP2023-2131
中图分类号： TP18   

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基金

国家自然科学基金(62076002,61402005,61972001);安徽省自然科学基金(2008085MF194,1308085QF114,1908085MF188);安徽省高等教育自然科学基金(KJ2013A015)
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