灰色决策问题的分析方法研究
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摘要
本文的工作可以分为以下几个部分:
1 研究了灰色决策问题的区间关联和区间聚类分析方法:提出了灰色区间关联系数公式和灰色区间相对关联系数公式,构建了几种关联度决策算法.对不完全信息下灰色区间关联决策方法进行了研究,首先对目标权重和决策偏好信息不完全的情况建立了灰色区间关联决策算法;其次进一步研究了方案目标值有空缺时的情况,给出了填补空缺的方法和理论依据,建立了基于满意度水平下的灰色区间关联算法;研究了灰色区间关联聚类决策方法;最后通过引入方案间优势强度、相对优势强度和优势比较矩阵等概念及其计算公式,对指标权重完全未知的情况,建立了特征向量决策算法. 应用实例说明了文中提出的灰色决策算法的合理性、实用性和有效性.
2 在经典灰色规划的基础上,对灰色动态规划、灰色多目标规划算法、灰色正项几何规划进行了研究:提出了灰色动态规划、θ动态定位规划及其最优解的概念,构建了灰色动态规划及θ动态定位规划最优解的算法. 对一般意义上的灰色多目标规划,提出了客观确定子目标权重的方法及修正方法,利用子目标的权重引入了各个子目标取最优值的白化权函数,构建了灰色多目标规划有效解及其θ定位规划最优解的算法. 提出了灰色正项几何规划、θ定位几何规划及其准优解和最优解的概念,构建了灰色正项几何规划准优解的算法. 算例说明了算法的合理性和可行性.
3 对灰色风险型决策方法进行了研究:提出了灰色多指标风险型决策的概念,对指标权重完全未知且指标值为区间灰数的风险型多指标决策问题,给出了灰色模糊关系法及双基点法两种决策方法,利用信息熵确定的属性权重使决策方法更符合客观要求. 提出了具有交易费用的灰色组合投资模型的有效解及其临界最优解和均值白化最优解的概念,并且指出了这些概念所对应的投资偏好,构建了带有交易费用的灰色组合投资模型的熵权分析算法. 应用实例表明了决策算法的合理性与可行性.
4 对灰色模糊决策方法进行了研究:提出了基于灰色模糊信息的多属性决策的概念,构建了灰色模糊多属性决策问题的算法,直接由灰色模糊决策矩阵确定变权的基础权重和上确界,使算法在理论上更加严谨可靠. 提出了灰色群决策问题的概念,给出了灰色群决策问题的解法,通过实例对解法的合理性进行了说明与分析. 建立了基于灰色模糊关系的多属性群体决策方法,分别对属性权重向量已知和未知
This dissertation is composed of six parts.
Part 1. The analytical methods of the grey interval incidence degree and grey interval cluster for grey decision-making are studied. The incidence degree coefficient formula and relative incidence degree coefficient formula for interval grey numbers are presented, and three types of incidence degree decision-making algorithms are put forward. Grey incidence decision-making with incomplete information is researched. Firstly, an algorithm is established to deal with the inadequacy of objective weight and preferential information of decision-making. Secondly, based on the satisfactory degree, an algorithm is established for grey interval incidence decision-making in the case of project objective value with null, and then with theory and method given to fulfill the null. Finally, the grey interval clustering decision algorithm is studied. Concepts and formulas are introduced for predominance strength, relative predominance strength and predominance comparative matrix between alternatives, and then an eigenvector decision algorithm is established for the case of the unknown attribute weight and preferential information of decision-making. Examples show the rationality, practicability and validity of the algorithms presented above.
Part 2. On the basis of classical grey programming, the grey dynamic programming, grey multiple objective programming and grey polynomial geometric programming are studied. Firstly, grey dynamic programming model, θ dynamic positioned programming model and the definition of their optimum solution are put forward. The grey dynamic programming algorithm and θ dynamic positioned programming algorithm are also developed. Secondly, a method to objectively determine objective weights of grey multiple objective programming is given,and whitenization weight function of sub-object for obtaining optimum values is introduced. An algorithm for obtaining optimal point of grey multiple objective programming is constructed. Finally, a model of grey polynomial geometric programming, a model of θ positioned geometric programming and their quasi-optimum solution or optimum solution are presented. At the same time, an algorithm for the problem is also developed. Examples are offered to show the rationality and validity of the algorithms presented above.
Part 3. Grey risk decision-making method is discussed. Firstly, a conception of grey
multi-criteria risk decision-making is offered, and the risk multi- criteria decision-making problems are studied in which criteria weights are unknown and criteria values are interval grey numbers. Two algorithms based on grey fuzzy relation and two points method are respectively given to get the priorities of alternatives. In these algorithms, criteria weights are obtained by the use of information entropy, which ensures that the algorithm confirms to objective desire. Then the definitions and investment priorities corresponding to them are given to explain efficient solution, critical optimum solution and mean whitenization optimum solution of grey portfolio selection model with transaction costs. An algorithm for grey portfolio selection model with transaction costs is presented. The given examples prove the rationality and the feasibility of the algorithms above.
Part 4. Grey fuzzy relation decision-making method is discussed. Firstly, based on the grey fuzzy relation, the conception of multiple attribute decision-making is presented, and a corresponding algorithm is developed which is more precise and reliable than those methods used before since its basic weight and upper bound are directly determined by grey fuzzy decision-making matrix. Secondly, the conception of grey group decision-making is put forward and the solutions to the problem are developed as well. The feasibility of the solution is shown by the example. Thirdly, a method for multi-attribute group decision-making is presented based on the theory of grey fuzzy relation and furthermore two practical algorithms are given, in which attribute weights are known o
1 研究了灰色决策问题的区间关联和区间聚类分析方法:提出了灰色区间关联系数公式和灰色区间相对关联系数公式,构建了几种关联度决策算法.对不完全信息下灰色区间关联决策方法进行了研究,首先对目标权重和决策偏好信息不完全的情况建立了灰色区间关联决策算法;其次进一步研究了方案目标值有空缺时的情况,给出了填补空缺的方法和理论依据,建立了基于满意度水平下的灰色区间关联算法;研究了灰色区间关联聚类决策方法;最后通过引入方案间优势强度、相对优势强度和优势比较矩阵等概念及其计算公式,对指标权重完全未知的情况,建立了特征向量决策算法. 应用实例说明了文中提出的灰色决策算法的合理性、实用性和有效性.
2 在经典灰色规划的基础上,对灰色动态规划、灰色多目标规划算法、灰色正项几何规划进行了研究:提出了灰色动态规划、θ动态定位规划及其最优解的概念,构建了灰色动态规划及θ动态定位规划最优解的算法. 对一般意义上的灰色多目标规划,提出了客观确定子目标权重的方法及修正方法,利用子目标的权重引入了各个子目标取最优值的白化权函数,构建了灰色多目标规划有效解及其θ定位规划最优解的算法. 提出了灰色正项几何规划、θ定位几何规划及其准优解和最优解的概念,构建了灰色正项几何规划准优解的算法. 算例说明了算法的合理性和可行性.
3 对灰色风险型决策方法进行了研究:提出了灰色多指标风险型决策的概念,对指标权重完全未知且指标值为区间灰数的风险型多指标决策问题,给出了灰色模糊关系法及双基点法两种决策方法,利用信息熵确定的属性权重使决策方法更符合客观要求. 提出了具有交易费用的灰色组合投资模型的有效解及其临界最优解和均值白化最优解的概念,并且指出了这些概念所对应的投资偏好,构建了带有交易费用的灰色组合投资模型的熵权分析算法. 应用实例表明了决策算法的合理性与可行性.
4 对灰色模糊决策方法进行了研究:提出了基于灰色模糊信息的多属性决策的概念,构建了灰色模糊多属性决策问题的算法,直接由灰色模糊决策矩阵确定变权的基础权重和上确界,使算法在理论上更加严谨可靠. 提出了灰色群决策问题的概念,给出了灰色群决策问题的解法,通过实例对解法的合理性进行了说明与分析. 建立了基于灰色模糊关系的多属性群体决策方法,分别对属性权重向量已知和未知
This dissertation is composed of six parts.
Part 1. The analytical methods of the grey interval incidence degree and grey interval cluster for grey decision-making are studied. The incidence degree coefficient formula and relative incidence degree coefficient formula for interval grey numbers are presented, and three types of incidence degree decision-making algorithms are put forward. Grey incidence decision-making with incomplete information is researched. Firstly, an algorithm is established to deal with the inadequacy of objective weight and preferential information of decision-making. Secondly, based on the satisfactory degree, an algorithm is established for grey interval incidence decision-making in the case of project objective value with null, and then with theory and method given to fulfill the null. Finally, the grey interval clustering decision algorithm is studied. Concepts and formulas are introduced for predominance strength, relative predominance strength and predominance comparative matrix between alternatives, and then an eigenvector decision algorithm is established for the case of the unknown attribute weight and preferential information of decision-making. Examples show the rationality, practicability and validity of the algorithms presented above.
Part 2. On the basis of classical grey programming, the grey dynamic programming, grey multiple objective programming and grey polynomial geometric programming are studied. Firstly, grey dynamic programming model, θ dynamic positioned programming model and the definition of their optimum solution are put forward. The grey dynamic programming algorithm and θ dynamic positioned programming algorithm are also developed. Secondly, a method to objectively determine objective weights of grey multiple objective programming is given,and whitenization weight function of sub-object for obtaining optimum values is introduced. An algorithm for obtaining optimal point of grey multiple objective programming is constructed. Finally, a model of grey polynomial geometric programming, a model of θ positioned geometric programming and their quasi-optimum solution or optimum solution are presented. At the same time, an algorithm for the problem is also developed. Examples are offered to show the rationality and validity of the algorithms presented above.
Part 3. Grey risk decision-making method is discussed. Firstly, a conception of grey
multi-criteria risk decision-making is offered, and the risk multi- criteria decision-making problems are studied in which criteria weights are unknown and criteria values are interval grey numbers. Two algorithms based on grey fuzzy relation and two points method are respectively given to get the priorities of alternatives. In these algorithms, criteria weights are obtained by the use of information entropy, which ensures that the algorithm confirms to objective desire. Then the definitions and investment priorities corresponding to them are given to explain efficient solution, critical optimum solution and mean whitenization optimum solution of grey portfolio selection model with transaction costs. An algorithm for grey portfolio selection model with transaction costs is presented. The given examples prove the rationality and the feasibility of the algorithms above.
Part 4. Grey fuzzy relation decision-making method is discussed. Firstly, based on the grey fuzzy relation, the conception of multiple attribute decision-making is presented, and a corresponding algorithm is developed which is more precise and reliable than those methods used before since its basic weight and upper bound are directly determined by grey fuzzy decision-making matrix. Secondly, the conception of grey group decision-making is put forward and the solutions to the problem are developed as well. The feasibility of the solution is shown by the example. Thirdly, a method for multi-attribute group decision-making is presented based on the theory of grey fuzzy relation and furthermore two practical algorithms are given, in which attribute weights are known o
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