考虑方案集信息非完全的群体决策理论及其应用研究

Under the assumption of perfectly rational economics, the information of alternatives is complete when one is making decisions. However, the inherent limitations of the human brain make human do decisions naturely under the conditions of limited information. So it is very important to study the group decision making theory with limited information of alternatives, especially in today's vast amounts of network information.. The project focuses on Group decision-making theory and its applications under the considerations of limited information of alternatives. (1) A new research on acceptable consistency or weak transitivity of reciprocal or fuzzy judgment matrices will be given. A new definition will be proposed for the acceptable consistency of reciprocal preference relations with the transitivity conditions. The quantity index will be given for the weak transitivity of fuzzy preference relations. A new definition will be presented for interval and triangular fuzzy number judgment matrices with acceptable consistency. (2) The method of constructing a collective preference relation in group decision-making will be studied. The credibility concept of expert opinions will be proposed and the optimization model of constructing a collective preference relation with credibility will be shown. The sufficient conditions of collective preference relations with acceptance consistency of weak transitibity. (3)The algorithm for group decision-making problems and its application in joint decision-making problems of network organizations will be studied. Based on dynamic information and the credibility of expert opinions, the algorithm for solving group decision-making problems will be established. The solving strategy for joint decision-making problems of network organizations will be given. The obtained results will provide decision makers with new ideas and methods.

完全理性经济学假设人类在做决策时备选方案的信息是完全的，而人脑固有的局限性使得人类本质上只能在有限信息条件下做决策，因此研究信息非完全确知条件下的群体决策理论显得非常重要，尤其在网络信息海量化的今天。. 本项目研究方案集信息非完全条件下的群体决策理论及应用，包括（1）互反或互补判断矩阵满意一致性或弱传递性的新研究，将给出带传递性条件互反判断矩阵满意一致性新定义，建立互补判断矩阵弱传递性的数量弱化指标，给出区间数和三角模糊数互反判断矩阵满意一致性的新定义。（2）群体决策综合矩阵构造方法研究，将建立专家意见的可信度概念和提出综合矩阵可信度最优的数学模型，给出综合矩阵满意一致性或弱传递性的充分条件。（3）群体决策问题算法及在网络组织联合决策问题中的应用研究，将建立基于动态信息和专家意见可信度的群体决策问题算法，给出网络组织联合决策问题的求解策略。研究成果将给决策者提供新理念和方法。

群体的意见往往认为比个体更具有智慧，在信息不确定、信息缺失和方案集不完全条件下的群体决策理论及应用问题的研究具有重要的理论和实际意义。本项目针对群体决策的若干基础性问题进行了开创性的研究，主要有：（1）研究了判断信息一致性的本质特征，提出了三个公理化特征刻画相对测度下判断信息的一致性。（2）模糊数判断矩阵的近似一致性新定义，提出模糊判断信息的不确定性与一致性的严密逻辑关系的不兼容性科学观点。建立了区间数和三角模糊数判断矩阵的近似一致性新定义。（3）原创性的提出了模糊数的柔度定义及计算公式，为粒计算和近似推理提供了新的量化指标。（4）基于粒子群优化算法提出了新的群体决策模型，为实现网络环境条件下的大群体决策和应急管理等问题的快速解决提供了智能决策方法。