群决策中梯形模糊互补判断矩阵的相容性及专家权重确定方法  

Compatibility and Expert Weight Determination Method of Trapezoidal Fuzzy Complementary Judgment Matrices in Group Decision Making

作　　者：刘万里 刘卫锋[1] 何霞[1] LIU Wanli;LIU Weifeng;HE Xia(School of Mathematics,Zhengzhou University of Aeronautics,Zhengzhou,450046,China)

机构地区：[1]郑州航空工业管理学院数学学院,河南郑州450046

出　　处：《郑州航空工业管理学院学报》2023年第5期100-107,共8页Journal of Zhengzhou University of Aeronautics

基　　金：河南省高等学校重点科研项目(20A110035);河南省重点研发与推广专项(212102210552)。

摘　　要：针对梯形模糊互补判断的群决策问题,研究了偏好信息的相容性以及专家权重问题。首先利用定积分的知识,分别给出了两个梯形模糊数间的相容性定义和两个梯形模糊互补判断矩阵之间的相容性定义;其次分别给出了群体相容度以及满意相容性概念;再次给出群体相容性检验方法;最后基于相容度确定出每个决策专家的评判权重。本方法不仅能解决单纯梯形模糊互补判断的专家权重,而且也能适用于三角模糊互补判断和区间数互补判断的专家权重,更重要的是能解决混合型模糊互补判断的专家权重问题。算例显示了本方法的有效性。In the context of group decision making with trapezoidal fuzzy complementary judgments,the compatibility of preference information and the determination of expert weights are studied.Firstly,the compatibility definitions between two trapezoidal fuzzy numbers and between two trapezoidal fuzzy complementary judgment matrices are given based on the knowledge of definite integrals.Secondly,the concepts of group compatibility and satisfactory compatibility are introduced.Thirdly,a method for testing group compatibility is presented.Finally,the evaluation weights of each decision expert are determined based on compatibility measures.This method not only solves the expert weight determination problem for simple trapezoidal fuzzy complementary judgments,but also applies to expert weight determination for triangular fuzzy complementary judgments and interval number complementary judgments.Moreover,it can handle the expert weight determination problem for mixed-type fuzzy complementary judgments.Case studies demonstrate the effectiveness of the proposed method.

关 键 词：互补判断矩阵 梯形模糊数 相容性 群决策 专家权重 

分 类 号：O223[理学—运筹学与控制论]