模糊判断信息不完全下控制不确定程度的群体决策模型研究

Employing uncertainty to deal with inconsistency and incompleteness of pairwise comparison matrices has received more and more attention in recent years. It is important to capture and control these uncertainties in group decision making with interval/triangular/trapezoidal fuzzy comparison matrices. After addressing limitations of the current research in the existing literature, the project aims to carry out an intensive and systematic investigation in this inceptive research field from input, processing and output of decision data. Based on our research achievements on geometric consistency of comparison matrices and fuzzy decision making, the applicants will introduce a new logical relation between consistency and acceptability, and establish uncertainty index based inconsistency measurement models and acceptability testing methods for different types of fuzzy comparison matrices. Uncertainty control based frameworks to evaluating missing values of incomplete fuzzy comparison matrices will be examined by constructing optimization models and using the heuristic method. As acceptability of pairwise judgments is a fundamental constraint to deriving a reliable and reasonable decision result, some acceptability-maintained aggregation operators and optimization models will be developed to fuse fuzzy comparison matrices for various group decision situations. By introducing a new notion of normalized acceptable fuzzy weights, transformation relations between priority weights and fuzzy judgments will be furnished and used to develop priority models of interval/triangular/trapezoidal fuzzy comparison matrices. It is expected that the proposed models will further develop and enrich the theory and practice of fuzzy AHP, and play an important role in improving the quality and effectiveness of group decision making.

采用不确定性捕捉与应对比较矩阵不一致性和不完全性，统筹考虑和控制不确定性程度是基于成对判断群决策的新兴和重要研究方向。本项目针对现有基于区间/三角/梯形模糊判断群决策研究中存在局限性，将从决策数据输入、加工与输出三个层面对这个课题进行系统深入研究。以申请人在几何一致性和模糊决策方面研究成果为基础，通过引入新的一致性和可接受性逻辑关系，提出控制不确定程度的模糊比较矩阵一致性理论，建立基于不确定程度的模糊比较矩阵不一致性测度和可接受性检验模型；研究具有不确定程度控制的缺失值求解理论和优化与启发式模型；考虑到可接性是判断信息基本约束，对不同群决策情景分别运用集结算子和优化方法构建保持可接性模糊比较矩阵集结模型；引入规范化可接受模糊权重概念，研究排序权重与模糊比较矩阵的转换关系，开发排序权重求解和层次总排序模型。其研究成果将发展与丰富模糊AHP的理论和实践，对提高群决策质量与有效性具有重要意义。

本项目开展的研究内容主要包括：(1) 控制不确定程度的区间/三角模糊层次分析方法(AHP)；(2) 控制不确定程度的区间模糊/直觉模糊AHP；(3) 判断信息不完全下基于区间/模糊AHP的群体决策模型及其应用研究。建立了区间/三角模糊互反比较矩阵一致性的公理化系统；构建了Saaty传递性等式的区间/三角模糊拓展模型；开发了区间/三角模糊互反比较矩阵排序权重解析解的计算公式；设计了区间/三角模糊互反比较矩阵的几何一致性指数模型；构建了控制不确定程度的区间/三角模糊互反比较矩阵可接受性检验模型；提出了控制不确定程度的区间/三角模糊AHP。构建了Tanino乘性传递性等式的区间模糊/直觉模糊/三角模糊的拓展模型；得到了区间模糊/直觉模糊/三角模糊互补比较矩阵排序权重解析解的计算表达式；给出了区间模糊/直觉模糊/三角模糊互补比较矩阵的一致性指数模型；建立了控制不确定程度的区间模糊/直觉模糊/三角模糊互补比较矩阵可接受性检验模型；提出了控制不确定程度的区间模糊/直觉模糊AHP。开发了判断信息不完全下基于区间/模糊AHP的群体决策模型，并开展了提出决策模型的应用研究。项目研究主要成果发表在《Information Sciences》、《IEEE Transactions on Fuzzy Systems》、《Computers & Industrial Engineering》、《Fuzzy Sets and Systems》、《International Journal of Production Research》、《Applied Soft Computing》、《Journal of Intelligent & Fuzzy Systems》等决策科学国际知名期刊上。在项目执行期，共发表SCI/SSCI期刊学术论文31篇；项目负责人入选爱思唯尔(Elsevier)2019年中国高被引学者 (决策科学) 榜单；已培养毕业研究生9名，获得1项决策支持系统的计算机软件著作权。