基于自信息熵的直觉模糊决策系统的属性约简  

Attribute reduction based on the self-information entropyof intuitionistic fuzzy decision systems

作　　者：尹晓君 冯涛[2] 张少谱 YIN Xiaojun;FENG Tao;ZHANG Shaopu(Department of Mathematics and Physics,Shijiazhuang Tiedao University,Shijiazhuang 050043,P.R.China;School of Sciences,Hebei University of Science and Technology,Shijiazhuang 050018,P.R.China)

机构地区：[1]石家庄铁道大学数理系,石家庄050043 [2]河北科技大学理学院,石家庄050018

出　　处：《重庆邮电大学学报（自然科学版）》2024年第3期513-523,共11页Journal of Chongqing University of Posts and Telecommunications(Natural Science Edition)

基　　金：国家自然科学基金项目(62076088);河北省自然科学基金项目(A2020208004)。

摘　　要：针对在直觉模糊集中,利用下近似构建的约简只考虑了下近似而忽略了上近似,从而导致一些信息丢失的问题,基于直觉模糊集的上、下近似提出了3种熵度量,并将其应用于直觉模糊决策信息系统的约简之中。在直觉模糊决策信息系统上定义用于描述直觉模糊关系的3种不确定性度量,分别为平均决策指数、平均安全决策指数以及平均风险决策指数,并在此基础上依次提出了条件信息熵、条件粗糙熵和自信息熵,基于自信息熵给出了相应的约简定义以及属性约简算法。在多个数据集上的实验表明,所提出的属性约简算法与其他算法相比,约简结果更具有优越性以及鲁棒性。In the context of intuitionistic fuzzy sets,the reduction based on lower approximation only considers the lower approximation and ignores the upper approximation,resulting in certain information loss.To address this issue,three entropy measures based on upper and lower approximations of intuitionistic fuzzy sets are presented and applied to the reduction of intuitionistic fuzzy decision information systems.Three uncertainty measures are defined on the intuitionistic fuzzy decision information system to describe intuitionistic fuzzy relationships,namely the average decision index,the average safe decision index,and the average risk decision index.Based on these measures,conditional information entropy,conditional rough entropy,and self-information entropy are subsequently introduced.Based on the self-information entropy,a definition of attribute reduction and an attribute reduction algorithm are proposed.Experiments on multiple datasets show that the proposed attribute reduction algorithm exhibits superior and robust reduction results compared to other algorithms.

关 键 词：属性约简 直觉模糊决策信息系统 条件信息熵 条件粗糙熵 自信息熵 

分 类 号：O236[理学—运筹学与控制论]