基于改进Min-Max权重优化模型的语意评价矩阵群决策研究  

Group Decision Making of Semantic Evaluation Matrix Based on Improved Min-Max Weight Optimization Model

作　　者：王韧 陈明[2] WANG Ren;CHEN Ming(School of Finance,Hunan University of Technology and Business,Changsha 410205;School of Mathematics and Statistics,Central South University,Changsha 410083)

机构地区：[1]湖南工商大学财政金融学院,长沙410205 [2]中南大学数学与统计学院,长沙410083

出　　处：《系统科学与数学》2021年第11期3181-3192,共12页Journal of Systems Science and Mathematical Sciences

基　　金：国家社科基金项目(19BJY161);湖南省自然科学基金项目(2021JJ30197)资助课题。

摘　　要：文章提出两个改进的Min-Max优化模型,用于解决多粒度语意评价矩阵的群决策问题.第一个模型用于确定多粒度语意评价矩阵的准则权重,其目标是使各专家对备选方案的实际评估值和综合每个专家的评估意见后所得的评估值之间的最大偏离取得最小值.第二个改进的Min-Max模型用于优化多粒度语意评价矩阵的专家权重,由于每个专家对每个方案的实际评估与最后的综合各专家的加权综合评估有偏离,模型的目标函数在于保证每个专家对各个方案的偏离之和最大的那个取得最小.由此得到对每个方案的综合评估.这种综合评估能够尽可能地综合了各专家的意见,提升了评估的科学和准确性.In this paper,two improved Min-Max optimization models are proposed to solve the group decision-making problem based on multi-granularity semantic evaluation matrix.The first model is used to determine the criterion weight based on multi-granularity semantic evaluation matrix,to minimize the maximum deviation between the actual evaluation value of each expert and the evaluation value obtained after synthesizing the evaluation opinions of each expert.The second improved MinMax model is used to optimize the weight of expert based on the multi-granularity semantic evaluation matrix.Considering that each expert’s actual evaluation of each scheme deviates from the final weighted comprehensive evaluation of each expert,the objective function of the model is to ensure that the maximum deviation sum of each expert to each scheme is minimized to obtain the comprehensive evaluation of each scheme.This kind of comprehensive evaluation can integrate the opinions of experts as much as possible,which can improve the credibility and accuracy of the evaluation.

关 键 词：多准则群决策 权重优化 语意评价矩阵 Min-Max模型 

分 类 号：O225[理学—运筹学与控制论]