基于区间值的广义多尺度决策系统及最优尺度组合选择  

Generalized Multi-Scale Decision System Based on Interval Value and Optimal Scale Combinations Selection

作　　者：任泽 李磊军[1,2] 米据生 李美争[3] REN Ze;LI Leijun;MI Jusheng;LI Meizheng(College of Mathematical Sciences,Hebei Normal University,Shijiazhuang 050024,China;Hebei Key Laboratory of Computational Mathematics and Applications,Shijiazhuang 050024,China;College of Computer and Cyberspace Security,Hebei Normal University,Shijiazhuang 050024,China)

机构地区：[1]河北师范大学数学科学学院,石家庄050024 [2]河北省计算数学与应用重点实验室,石家庄050024 [3]河北师范大学计算机与网络空间安全学院,石家庄050024

出　　处：《西南大学学报（自然科学版）》2023年第3期19-33,共15页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金项目(61502144,62076088,12101182);河北省高等学校科学技术研究项目(BJ2019014)。

摘　　要：多尺度决策系统基于多粒度思想对数据进行不同角度、深层次的分析与处理.目前,多尺度决策系统主要处理单值形式的数据,但在许多实际问题中,决策系统中的数据往往以区间值的形式存在.因此,将经典的多尺度决策系统推广到区间值上具有一定的意义.本研究定义了广义多尺度区间值决策系统的概念;基于Jaccard相似率推广了计算多属性下对象之间的相似度,以构造θ-相容关系;讨论了保持4种分布协调性相互等价的θ取值;证明了在不协调广义多尺度区间值决策系统中,任取一个θ值获得的最优尺度组合与取关于θ的某个区间范围获得的最优尺度组合相同.Based on the idea of multi-granularity,multi-scale decision system analyzes and processes data from different perspectives and in different depths.At present,it mainly deals with data sets of discrete attribute values.As an extension of single valued decision system,interval valued decision system can be better describe the phenomenon and reflect the uncertainty of information.Therefore,it is meaningful to extend the generalized multi-scale decision system to interval value.In the first part,the concept of generalized multi-scale interval valued decision system was defined.Then,in order to construct θ-tolerance relationship,the Jaccard similarity ratio was extended to the similarity between objects under multiple attributes.Secondly,discussion on the value of θ that makes the four kinds of distribution coordination equivalent to each other was made.Finally,it was proved that in an inconsistent generalized multi-scale interval valued decision system,taking any value of θ is the same as taking an interval range about the value to obtain the optimal scale combination.

关 键 词：多尺度决策系统 区间值 相似度 θ-相容关系 尺度组合 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]