基于区间粗糙数相似度的多准则群体决策方法及其应用  

Multi-criteria Group Decision-making Method Based on the Interval Rough Number Similarity and Its Application

作　　者：刘启函 叶国菊[1] 刘尉[1] 赵大方 LIU Qihan;YE Guoju;LIU Wei;ZHAO Dafang(College of Sciences,Hohai University,Nanjing 210098 China;School of Mathematics and Statistics,Hubei Normal University,Huangshi 435002 China)

机构地区：[1]河海大学理学院,江苏南京210098 [2]湖北师范大学数学与统计学院,湖北黄石435002

出　　处：《西华大学学报（自然科学版）》2022年第5期104-112,共9页Journal of Xihua University:Natural Science Edition

基　　金：国家冰川冻土沙漠科学数据中心开放基金(2021kf03)。

摘　　要：针对权重未知的区间粗糙数多准则群体决策问题,提出一种基于相似度最大化的群体决策方法。文章对区间数构造区间粗糙数的方法进行改进,进一步定义区间粗糙数相似度公式,并给出相应的性质;以各方案与标准方案相似度最大化及熵值最大为目标,建立多目标优化模型求解准则权重,利用区间粗糙数算子求出方案的综合决策值,进而由区间粗糙数可能度和排序向量模型获得方案的排序结果。最后,通过投资实例证明该方法是有效的、合理的。For the multi-criterion group decision-making problem of interval rough number with unknown criteria weight,a group decision-making method based on the maximize similarity is proposed.Firstly,the method of constructing interval rough numbers is improved and the interval rough number similarity formula is defined where the corresponding properties are given.Secondly,a multi-objective optimization model is constructed to solve criterion weight with the maximum entropy and the similarity maximizing between each alternative and the standard alternative.Then,the comprehensive decision value of each alternative is calculated by the interval rough number operator gathering expert weights and criterion weights,and the ranking result is obtained by the interval rough probability degree and the ranking vector model.Finally,an investment decision example is given to verify the effectiveness and rationality of the method.

关 键 词：区间粗糙数 多准则决策 相似度 可能度 群体决策 

分 类 号：O29[理学—应用数学] C934[理学—数学] TP18[经济管理—管理学]