基于模糊层次分析法的群体决策理论及其应用研究

With the socio-ecomomic development, one has paid much attention to theories, methodology and applications of group decision making. However, due to the complexity of real-world and the fuzziness of man decision, it is more natural and reasonable for the decision maker to evaluate his/her judgements by using interval numbers,triangular fuzzy numbers and trapezoidal fuzzy numbers and so on. So the analytic hierarchy process (AHP) will be extended to the Fuzzy AHP. Group decision making based on Fuzzy AHP should be further studied since the corresponding research work is very few. The consistency study of preference relations is a main issue of group decision making.. Based on FAHP, here we study group decision making problems and their applications. Firstly, the consistency analysis of uncertain preference relations are made by making use of physical psychology and logical relation. One finds the conditions of consistent socail preference relations by probing. So the group decision making problems are addressed when the decision makers give different type of uncertain preference relations. Secondly, based on the consistency and optimization theories, some models for evaluating incomplete information in incomplete uncertain preference relations are proposed. Group decision problems are further investigated when the judgement of the decision makers are given by using incomplete uncertain preference relations. Finally, the theory and method of group decision making based on FAHP are utilized to deal with the evaluation of science and technology projects. The obtained results will perfect Fuzzy AHP, enrich the theory of group decision making, and give some theoretical bases for the decision makers.

随着社会经济的发展，群体决策理论、方法与应用研究已经引起人们极大的关注。然而，由于现实环境的复杂性和人类判断的模糊性，决策者的偏好信息采用区间数、三角模糊数和梯形模糊数等不确定数来表示更加自然合理，经典的层次分析法有待扩展为模糊层次分析法。目前基于模糊层次分析法的群体决策理论与应用有待进一步研究，其中判断矩阵的一致性是研究的难点和热点。.本项目研究基于模糊层次分析法的群体决策理论及其应用。主要有：（1）应用物理心理学和逻辑关系研究不确定数判断矩阵的一致性问题，采用试探的方式找到综合矩阵的一致性条件，解决含有不同类型不确定数判断矩阵的群体决策问题；（2）采用一致性定义和最优化理论建立残缺不确定数判断矩阵中残缺信息估计的数学模型，解决含有残缺不确定数判断矩阵的群体决策问题；（3）新的群体决策理论在科技项目评估中的应用。研究成果将完善模糊层次分析法，丰富群体决策理论，为决策者提供理论依据。

群体决策理论、方法与应用研究具有重要的理论和实际意义。为了模拟现实环境的复杂性和人类判断的模糊性，决策者的偏好信息往往采用区间数、三角模糊数和梯形模糊数等来表示，于是经典的层次分析法有必要扩展为模糊层次分析法。本项目研究模糊环境下的群体决策理论及其在虚拟企业伙伴选择中的应用，主要获得了以下一些成果：..1、采用模糊集理论和偏好关系的逻辑特性，提出了一致性三角模糊数互反判断矩阵的新定义，并研究了其性质。克服了Buckley[Fuzzy Sets and Systems, 1985, 17: 233–247]给出的一致性三角模糊数互反判断矩阵定义的不足，指出了Wang和Chen[Information Sciences, 178(19): 3755–3765]一致性定义属性证明过程中的错误。然后，提出了构建一致性三角模糊数互补判断矩阵的方法，研究了当单个决策者给出三角模糊数互补判断矩阵时的群体决策问题，从而解决了相应的群体决策问题。主要成果发表在《European Journal of Operational Research》上。..2、由于经历、知识和观点不同，不同专家给出不同的判断矩阵, 研究了含有区间数互反和互补判断矩阵的群体决策问题。首先基于积型一致性建立了区间数互反和互补判断矩阵的转化公式，然后提出了一个新的OWA集成算子，此算子的特点就是专家的矩阵一致性程度高那么获得权重也就高，最后研究区间数综合矩阵的满意一致性。主要成果发表《Fuzzy Sets and Systems》和《Applied Mathematical Modelling》上。..3、对于一个实际的决策问题来说，决策者可能由于知识的不完备而不能给出一个完整的判断矩阵，也就是说给出的判断矩阵中有些信息是残缺的。基于理想点方法，提出了含有残缺区间数互补判断矩阵的群体决策方法。首先建立估计残缺信息的优化数学模型，还有提出了相似度公式，然后给出了指引的OWA集成算子，此算子以相似度为准则构建集成算子的权重向量，从而解决了相应群体决策问题。主要成果发表《IEEE Transactions on Cybernetics》和《International Journal of Intelligent Systems》上。