广义多尺度多重集值决策系统的最优尺度约简  

Optimal Scale Reducts for Generalized Multi-scale Multiset-Valued Decision Systems

作　　者：刘梦欣 谢祯晃 吴伟志 朱康 LIU Mengxin;XIE Zhenhuang;WU Weizhi;ZHU Kang(School of Information Engineering,Zhejiang Ocean University,Zhoushan 316022)

机构地区：[1]浙江海洋大学信息工程学院,舟山316022

出　　处：《模式识别与人工智能》2025年第1期2-21,共20页Pattern Recognition and Artificial Intelligence

基　　金：国家自然科学基金项目(No.12371466,62076221)资助。

摘　　要：多尺度数据的知识表示与知识获取是现阶段多粒度计算研究的一个重要方向.在分析多尺度数据时,一个关键问题是最优尺度组合的选择,其目的是选择合适的子系统用于最终决策.因此文中针对多尺度多重集值数据的知识获取问题展开研究.首先,基于海林格距离,在广义多尺度多重集值决策系统中构造不同尺度组合下对象集上的相似关系,给出广义多尺度多重集值决策系统的信息粒表示.然后,在协调广义多尺度多重集值决策系统中,定义最优尺度约简与熵最优尺度约简的概念,证明最优尺度约简与熵最优尺度约简的等价性.在不协调广义多尺度多重集值决策系统中,引入广义决策函数,给出广义决策最优尺度约简的定义.进一步地,基于条件熵和广义决策函数,分别给出熵最优尺度约简搜索算法和广义决策最优尺度约简搜索算法.最后,提出构造广义多尺度多重集值决策系统的方法,并通过实验验证文中最优尺度约简算法的有效性和合理性.The knowledge representation and the knowledge acquisition of multi-scale data are crucial research directions in multi-granularity computing.While analyzing multi-scale data,a key issue is the selection of the optimal scale combination,with the aim of choosing a suitable subsystem for the final decision.To solve the problem of knowledge acquisition from multi-scale multiset-valued data,at first,similarity relations determined by the set of objects under different scale combinations are constructed based on Hellinger distance in generalized multi-scale multiset-valued decision systems,and the information granule representation is provided.Second,the concepts of optimal scale reducts and entropy optimal scale reducts are defined in consistent generalized multi-scale multiset-valued decision systems,and the equivalence between the optimal scale reducts and the entropy optimal scale reducts is proven.In inconsistent generalized multi-scale multiset-valued decision systems,the definition of generalized decision optimal scale reducts is proposed by introducing generalized decision functions.Furthermore,by employing conditional entropies and generalized decision functions,search algorithms of entropy optimal scale reducts and generalized decision optimal scale reducts are designed.Finally,a method of constructing generalized multi-scale multiset-valued decision systems is proposed,and the experiments demonstrate the validity and rationality of the proposed algorithms.

关 键 词：属性约简 条件熵 广义多尺度决策系统 多重集 最优尺度约简 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]