基于熵和可信度的图模糊多属性AQM决策方法  

Picture Fuzzy Multiple Attribute AQM Decision Making Method Based on Entropy and Credibility

作　　者：王磊 罗娜[2] WANG Lei;LUO Na(Department of Basic Teaching,Liaoning Technical University,Huludao 125105,China;College of Science,Liaoning Technical University,Fuxin 123000,China)

机构地区：[1]辽宁工程技术大学基础教学部,辽宁葫芦岛125105 [2]辽宁工程技术大学理学院,辽宁阜新123000

出　　处：《数学的实践与认识》2024年第11期23-37,共15页Mathematics in Practice and Theory

基　　金：辽宁省教育厅科学研究经费项目(LJ2020JCL018)。

摘　　要：针对决策信息为图模糊数,属性权重未知的多属性决策问题,提出了扩展的图模糊多属性AQM(Alternative queuing method)决策方法.首先,构造图模糊Zhenyuan积分并提出一种新的图模糊熵,由此建立熵测度权重模型.其次,为进一步提高决策的有效性,将信任函数与新提出的散度结合得到证据体的支持度和可信度权重,对熵权重和可信度权重加权计算得到综合权重.再次,在决策过程中将图模糊矩阵转化为得分矩阵,同时为避免传统的AQM方法中[0,1)优先关系矩阵区分不明确,采用可能度替代0-1偏好关系得到[0,1]可能度矩阵,进一步确定方案的综合指标并对方案进行排序.最后,通过算例分析说明本文方法的有效性,并通过灵敏度分析与对比分析表明所提方法的可行性和优点.To address the multiple attribute decision-making problem with picture fuzzy numbers and unknown attribute weights,an extended picture fuzzy multiple attribute AQM(Alternative Queuing Method)decision making approach is proposed.Firstly,we construct the picture fuzzy Zhenyuan integral and introduce a new picture fuzzy entropy.Based on this,we establish an entropy measure weight model.Secondly,to enhance decision-making effectiveness,the trust function is combined with the newly proposed divergence to calculate the support and credibility weights of the body of evidence,and the entropy weight and credibility weight are weighted to obtain the comprehensive weight.Thirdly,in the decision-making process,we transform the picture fuzzy matrix into a score matrix.At the same time,to avoid the ambiguity of the O,1 priority relation matrix in the traditional AQM method,the possibility degree replaces the 0-1 preference relation to get the[0,1]possibility matrix,to further determine the comprehensive index of the scheme and sort the scheme.Finally,we give an example to illustrate the effectiveness of the proposed method and demonstrate the feasibility and advantages of the proposed method through sensitivity analysis and comparative analysis.

关 键 词：图模糊集 熵 可信度 AQM 可能度 多属性决策 

分 类 号：O225[理学—运筹学与控制论] O159[理学—数学]