基于多重集值信息系统的三支决策  

Three-way Decision Based on Multiset-valued Information Systems

作　　者：陈跃 王宣 Chen Yue;Wang Xuan(School of Mathematics and Statistics,Liupanshui Normal University,Liupanshui 553004,China)

机构地区：[1]六盘水师范学院数学与统计学院,贵州六盘水553004

出　　处：《六盘水师范学院学报》2022年第3期61-73,共13页Journal of Liupanshui Normal University

摘　　要：三支决策是一种三分而治的思想策略已经被证明是处理信息系统中不确定性的有效工具。由于多重集能够呈现更加全面完整的信息,通过将单值信息系统推广到多重集值信息系统,建立了基于多重集值信息系统的三支决策模型。首先,将基于多重集距离的相似性测度作为评价函数,建立了[0,1]多重集值信息系统上的三支决策模型。其次,指出[0,1]多重集值信息系统可以用模糊多重集代替,以此可以建立模糊多重集上的三支决策模型。最后,基于模糊多重集的交、并、以及差运算,提出了三种新的相似性测度,以弥补基于多重集距离的相似性测度在某些应用中的缺陷。Three-way decision is a philosophy of thinking in threes and then acting that has been proved to be an effective tool for dealing with uncertainty in information systems.Since multisets can provide more com⁃plete information,a new model of three-way decision based on multisets-valued information systems is estab⁃lished by extending the single-valued information systems to the multisets-valued information systems.Firstly,using the similarity measure based on the distance of multisets as the evaluation function,the model of three-way decision on[0,1]multisets-valued information systems is established.Secondly,this paper points out that the[0,1]multisets-valued information system can be replaced by a series of fuzzy multisets,and estab⁃lishes a model of three-way decision on fuzzy multisets.Finally,based on the intersection,union and subtrac⁃tion operation of fuzzy multisets,three new similarity measures are proposed,which successfully make up the defects of similarity measures based on the distance of multisets in some applications.

关 键 词：三支决策 多重集 模糊多重集 相似性测度 

分 类 号：O225[理学—运筹学与控制论]