粗糙集的信息损失及其多阶定义  

Information loss of rough sets and their multi-order definitions

作　　者：邓大勇[1,2,3] 汪杰[2] DENG Dayong;WANG Jie(Xingzhi College,Zhejiang Normal University,Lanxi 321100,China;School of Computer Science and Technology,Zhejiang Normal University,Jinhua 321004,China;Key Laboratory of Intelligent Education Technology and Application of Zhejiang Province,Zhejiang Normal University,Jinhua 321004,China)

机构地区：[1]浙江师范大学行知学院,浙江兰溪321100 [2]浙江师范大学计算机科学与技术学院,浙江金华321004 [3]浙江师范大学浙江省智能教育技术与应用重点实验室,浙江金华321004

出　　处：《浙江师范大学学报（自然科学版）》2023年第4期379-384,共6页Journal of Zhejiang Normal University:Natural Sciences

基　　金：浙江省科技计划资助项目(2020C35066)。

摘　　要：粗糙集的模型众多,但缺乏对这些模型的信息损失研究.针对粗糙集模型的信息损失问题,提出了一种计算信息损失的方法,根据信息损失的不同将粗糙集模型分为3类:零阶粗糙集、一阶粗糙集和二阶粗糙集.首先,针对粗糙集模型,给出了计算信息损失的方法;其次,定义了比零阶粗糙集信息损失少的一阶粗糙集,并定义了它们的属性约简;最后,定义了无信息损失的二阶粗糙集,并给出了其属性约简的定义.研究成果为研究粗糙集模型提供了一个新的视角,并为粗糙集和粒计算的研究者提供一些启示.There were established many rough set models in relevant literature,but none of their information loss had been investigated.In order to address information loss in rough set models,a method of computing information loss for rough set models was presented,and then rough set models were divided into 3 categories:zero-order rough sets,first-order rough sets and second-order rough sets.Firstly,the information loss for rough set models was computed in the terms of their definitions.Secondly,first-order rough sets were defined,which lost less information than zero-order rough sets,then their corresponding attribute reductions were defined.Thirdly,second-order rough sets were defined,which had no information loss,and then their corresponding attribute reductions were also defined.A novel perspective to investigate rough set models was provided,and some heuristic information was also suggested for rough sets and granular computing researchers.

关 键 词：粗糙集 信息损失 零阶粗糙集 一阶粗糙集 二阶粗糙集 

分 类 号：TP393[自动化与计算机技术—计算机应用技术]