基于偏序集的PROMETHEE方法优化研究

Study on PROMETHEE Method Optimization Based on Poset

尽管PROMETHEE是当前最受欢迎的多准则决策方法之一,但在实践应用过程中,模型的应用范围与质量依然受制于指标权重问题.一些常用的赋权方法,不仅没有解决不确定权重问题,反而增加了决策风险.在偏序集相关定理的基础上,给出权重的定性信息即权重次序,由流出矩阵、流入矩阵和净流矩阵等定义,得到了PROMETHEE的偏序集表达形式.当流入和流出之和为常数时,证明了模型存在对偶性质.根据对偶性质,简化了PROMETHEE方法的分析步骤,删减模型冗余信息.应用偏序集表示的PROMETHEE,突破了模型没有具体权重便无法应用的思维定势,解决了模型赋权困难,增强了模型的鲁棒性,拓展了模型处理数据类型的范围.

Although PROMETHEE is one of the most popular multi-criteria decision making methods at present,its application scope and quality are still subject to the index weight in the practical application.Some frequently-used weighting methods not only fail to solve the problem of uncertain weight,but also increase the decision-making risk.On the basis of the correlation theorems of Poset,coupled with the qualitative information of weight-weight order,the Poset expression of PROMETHEE is obtained by means of such definitions as outflow matrix,inflow matrix and net current matrix.If the sum of inflow and outflow is constant,it proves that the model has the duali-ty.According to the dual nature,the analysis steps of the PROMETHEE method are simplified with the redundant information deleted.The PROMETHEE model expressed by Poset breaks the mind-set that the method cannot be used without specific weights,with the difficulty of model weighting overcome.Meanwhile,it also enhances the robustness of the model and expands the data type scope.