基于两阶段优化的多属性决策法及其解的理论证明

Multi-attribute decision-making approach and theoretic proof of its solution based on two-phase optimization

针对只有部分权重信息(区间数),属性值为定值的多属性决策问题。先从局部考虑,建立一个目标规划模型,通过求解这个模型获得各方案的理想属性权重;再从全局考虑,建立一个二次规划模型,并对二次规划的最优解的存在性进行了理论证明。且给出了综合属性权重的求解公式,从而得到各方案的综合属性值,并以此对方案进行排序或择优。通过实例说明模型及方法的可行性和有效性。

The multi-attribute decision-making problems, in which the attribute weights are partly known （interval numbers） and the attribute values are numeric are investigated. Firstly, a linear objective programming model is established by considering in local and the ideal attribute weight of each alternative is obtained by solving the model. Secondly, a quadratic programming model with the constraints is established by considering in whole and the existence of optimum solution to the corresponding quadratic programming model is proved. Furthermore, the solving formula of the complex attribute weights is given, thus the complex attribute value of each alternative is obtained. Based on these values, the prioritizing or optimization for alternatives is made. Finally, a practical example is given to show the feasibility and availability of the developed model and method.