信息不完全的群体语言决策方法研究

【作者】 孙超；

【导师】 王坚强；

【作者基本信息】 中南大学 ， 管理科学与工程， 2005， 硕士

【摘要】 在社会经济生活中,存在大量群体语言决策问题。由于决策问题自身的模糊性和不确定性,因而决策者权重信息、决策准则信息不完全,以及决策者给出的评价值不能完全确定或者缺失的群体语言决策问题大量存在。因此对信息不完全确定条件下的群体语言决策理论与方法进行相关研究具有重要的理论和实践意义。本文研究了几类信息不完全确定群体语言决策问题,建立了相应的决策模型,并将其转化为线性规划模型、非线性规划模型、非线性混合0-1规划模型、非线性整数规划模型。根据优化理论和优化算法对其进行求解。其主要成果如下: (1)建立了决策者权重信息为确定数值、决策者的评价偏好为语言值且信息不能完全确定或者不能给出的基于方案之间相互比较的群体语言决策模型,并将其转化为线性规划模型直接求解。 (2)建立了决策者权重信息为数值且信息不完全、决策者的评价偏好为语言值且信息不能完全确定或者不能给出的基于方案之间相互比较的群体语言决策模型,并将其转化为非线性规划模型,并利用惯性权重粒子群算法进行求解。 (3)建立了决策者和评价准则的权重信息为数值且信息不完全、决策者的评价偏好为语言值且信息完全确定或者信息不能完全确定或者缺失的多准则群体语言指派决策模型,并将其转化为非线性混合整数规划模型,利用惯性权重粒子群算法结合匈牙利算法进行求解。 (4)建立了决策者、评价准则的权重信息为语言值且信息不完全、决策者的评价偏好为语言值且信息完全确定的多准则群体语言指派决策模型,并将其转化为非线性整数规划模型,提出了基于遗传交叉思想的交叉粒子群算法和结合匈牙利算法联合求解所得模型的方法。 (5)建立了决策者、评价准则的权重信息为数值且信息不完全、决策者的评价偏好为语言值且信息不能完全确定或者不能给出的类间有优序的多准则群体语言聚类决策模型,并根据K-均值的思想利用惯性权重粒子群算法进行聚类;更多还原

【Abstract】 In the social and economic activities, it is common that people will encounter a great deal of group decision-making problems with linguistic information. There are many methods proposed to deal with the linguistic information of the group decision-making factors. The method of transforming the linguistic information into two tuple is adopted in this paper, which can prevent the linguistic information from being twisted and lost. Because of the complexity and vagueness of the problems to be decided, it is normal that some information of the decision-making factors, such as the weights and the preference values given by the decision-makers, may be incomplete, and on such group decision-making problems with linguistic information, few literatures are focused, so it is significant and meaningful to do some researches on the theory and methods of the linguistic group decision-making problems, which having incomplete information about the decision making factors. This paper have researched a few types of such problems, and the corresponding models have been created and then worked out on the basis of the latest optimization theories and the popular optimizing algorithms. And the details are as follows:(1) A linear programming model is created and worked out directed by programming in the environment of Matlab7.0 for such a group decision-making problems with linguistic information, in which the preference information are obtained according to comparing any two alternatives by the decision-makers, and may take the form of standard linguistic evaluation grade, or may be between two continuous standard linguistic evaluation grade, or may be not given, and the weights of the decision-makers are numeric and certain.(2) As concerning such decision making problems as mentioned above, when the weights of the decision-makers are uncertain and numeric, then a nonlinear programming model is created and worked out with the improved Particle Swarm Optimization Algorithm.(3) As for the group multi-criteria linguistic assignment problem with incomplete certain information, in which the decision-makers’ weightsand the evaluation criteria’s weights are numeric and uncertain, andrthe assessment information may be between two continuous linguistic assessment grades or not be given by the decision makers, according to the function A and A"1 of two tuple, a nonlinear mixed integral programming model is constructed and worked out with the improved Particle Swarm Optimization Algorithm and Hungary Algorithm.(4) As concerning such decision-making problems as mentioned above, when the decision-makers’ weights and the evaluation criteria’s weights are linguistic and uncertain, a nonlinear integral programming model is constructed and worked out with the proposed Particle Swarm Optimization Algorithm combined with the ideal of -the Genetic Algorithm and Hungary Algorithm.(5) As for the group multi-criteria linguistic ordered clustering problems with incomplete certain information, in which the decision-makers’ weights and the evaluation criteria’s weights are numeric and uncertain, and the assessment information may be between two continuous linguistic assessment grades or not be given by the decision makers, the improved Particle Swarm Optimization Algorithm is adopted to solve such problems according to the way the K-means does.更多还原