节点文献
基于模糊决策矩阵的多属性决策方法研究
A Study on the Method of Multiple Attributes Decision Making Based on Fuzzy Decision Making Matrix
【作者】 高岩；
【导师】 周德群；
【作者基本信息】 南京航空航天大学 ， 管理科学与工程， 2010， 博士
【摘要】 多属性决策是多目标决策发展过程中形成的一个分支,广泛的应用于工程、社会、经济、管理和政治诸多领域中。由于现实决策问题的复杂性和决策环境的不确定性以及人类思维的模糊性,使得多属性决策的理论和方法都已经远远不能满足实际问题的需要,因此,对多属性决策理论和方法的优化、改进具有十分重要的必要性。本文以模糊数学为基础,基于模糊决策矩阵,利用计算机技术与最优化工具,从以下几个方面对多属性决策的方法进行了探索性的研究。(1)研究了基于区间数模糊决策矩阵的多属性决策方法。针对完整的区间数互补判断矩阵,提出了区间数标准型的概念,根据标准型的表示形式划分互补判断矩阵,进行一致性分析,通过建立最优化模型给出了决策的排序方法;在信息不完全即"贫信息"的情况下,结合灰色关联度、理想解法和误差传递公式,提出了区间数模糊决策矩阵的EA-TOPSIS方法;针对残缺区间数互补判断矩阵,在完全一致性和满意一致性下分别计算出了残缺区间数的具体数值,在填补残缺元后的随机互补判断矩阵基础上,结合Q型聚类方法、期望互补判断矩阵向量、灰色关联度最终给出决策者的排序向量。(2)研究了基于直觉模糊决策矩阵的多属性决策方法。利用Choquet模糊积分作为属性间关联的加权平均(WAA)算子的扩展,集结直觉模糊信息,构建了一种基于属性间关联的非线性规划模型;应用决策合理性标准的思想,克服了模糊决策矩阵赋权方法的弊端,将组合赋权的对象从有限拓展到了无限,给出了一种在属性权重未事前确知且存在关联的直觉模糊多属性决策组合赋权的新方法。(3)研究了基于三角模糊数直觉模糊决策矩阵的多属性决策方法。在三角模糊数直觉模糊数运算法则的基础上,构建了三角模糊数直觉模糊信息的R-TIOWA算子、R-TIWGA算子和R-TIOWGA算子;基于这些关联集成算子,引入了λ模糊测度,通过R-变权和R-状态变权理论,给出了三角模糊数直觉模糊决策矩阵的关联变权MADM方法;考虑了带概率的三角模糊数直觉模糊决策矩阵群决策的熵权法。(4)研究了基于梯形模糊数决策矩阵的多属性群决策方法。在属性权系数和决策者权系数信息都不完全的情况下,引入心态指标,将模糊语言的梯形模糊数决策矩阵转化为带心态指标的决策矩阵,对决策者的心态指标进行集成得到群体风险态度,进而得到方案的优劣排序;在上述基础上,提出一了种FL-DEMTEL方法,计算出影响因素的中心度和原因度,确定群决策因素的归属问题。(5)研究了基于模糊决策矩阵多属性决策方法在煤炭企业节能减排绩效评价中的应用问题。讨论了企业节能减排绩效评价的背景,说明了节能减排的意义;在分析现有节能减排绩效评价指标体系的基础上构建了煤炭企业节能减排绩效评价的指标体系;利用基于模糊决策矩阵的多属性决策方法评价了煤炭企业节能减排的绩效问题。
【Abstract】 Multiple arributes decision making is a branch of the multiple objective decision making, which is widely used in a many areas, such as engineering, society, economics, management and politics.Due to the complexity of real decision making, uncertainty of the decisiom evironment and ambiguty of humen thinking, the theory and method of multiple arributes decision making can not satisfy the needs of the practical questions. So it is very necessary to optimize and improve the theory and method of multiple arributes decision making. By computer technology and optimization tools, this paper researches the method of multiple arributes decision making based on fuzzy mathmatics and fuzzy decisiom matrix.(1)Study on the method of multiple arributes decision making based on interval number fuzzy decision making matrix. First of all, the definition of the standard form for interval numbers is proposed. According to this, the complementary judgment matrix is divided into the lower limit matrix and interval span matrix, and the consistency and weak consistency for the interval number fuzzy judgment metrics are analysised. Based on the consistency, the priority of the interval number fuzzy judgment metrics is proposed. Second under incomplete information, a new method of EA-TOPSIS for the interval number fuzzy decision making matrix is given. Finally the calculation of incomplete element about incomplete interval number fuzzy judgment matrix is researched. Under complete consistence and satisfaction consistence, the incomplete element is got. Base on these, the new priority method of the decision making is proposed by Q cluster analysis and grey correlation relative degree.(2)Study on the method of multiple arributes decision making based on intuitionistic fuzzy decision making matrix. Using Choquet fuzzy integral as a weighted average of attribute relations (WAA) operator expansion, assembly intuitionistic fuzzy information and constructe nonlinear programming model based on interaction of attributes; applicating reasonable standards of ideological decision-making to overcome the fuzzy weights decision matrix defects, the objects of combination weighting are expanded from limited to unlimited, a mathematical model of combination weighting for multiple attribute decision making with intuitionistic fuzzy information is established.(3)Study on the method of multiple arributes decision making based on triangular fuzzy number intuitionistic fuzzy decision making matrix. Under algorithm of triangular fuzzy number intuitionistic information, some new aggregation operators with interaction are developed, such as triangular fuzzy number intuitionistic fuzzy ordered weighted average operation with interaction(R-TPIOWA), triangular fuzzy number intuitionistic fuzzy weighted geometric average operation with interaction(R-TPIWGA) and triangular fuzzy number intuitionistic fuzzy ordered weighted geometric average operation with interaction (R-TPIOWGA). And a MADM method with variable weight of triangular fuzzy number intuitionistic fuzzy decision matrix is given. At last, the entropy method of triangular fuzzy number intuitionistic fuzzy matrix in the group decision making is proposed.(4)Study on the method of multiple arributes decision making based on trapezoidal fuzzy decision making matrix. Index of attitude is introduced, through which the trapezoidal fuzzy judgment matrix is transformed into the decision with index of attitude. The weights of the attribute and decision makers is obtained by solving the optimization problem. The priorities are given through the group risk attitude. And a new FL-DEMATEL method is made to calculate the cause degree and affect degree of the affecting factors for analysis of the relationship between the factors of the group decision making problems.(5)Study on application of multiple arributes decision making based on fuzzy decision making matrix in performance evaluation of coal enterpises energy saving and emission reduction. Discuss the background for performance evaluation of coal enterpises energy saving and emission reduction and explain the meaning of energy saving and emission reduction.The indicator system of performance evaluation of coal enterpises energy saving and emission reduction is established. Using the method of multiple arributes decision making based on fuzzy judgment matrix to evaluate the performance of coal enterpises energy saving and emission reduction.