序数权重统一表示下的权重稳健性Hasse图分析

Analysis of Hasse Graphs with Uniform Representation of Ordinal Weights

认识多种序数赋权方法的共性,有助于摆脱方法选择困扰,增强其实用效果。首先以线性函数为目标函数,以权重关系构造约束条件,建立线性规划。在此基础上证明了任意权重均可由线性规划的极值点集来表示,揭示了序数权重实质上是极值点的加权线性组合。进一步针对赋权方法稳健性不足的问题,利用极值点构建偏序关系,通过Hasse图增强权重排序的稳健性。实例分析表明,尽管序数权重不同,但与偏序方法相结合,均能得到类似的分析结果。

It is helpful to get rid of the puzzle of method selection and enhance its practical effect to recognize the commonness of several ordinal weighting methods.Firstly,linear programming is established by taking linear function as objective function and constructing constraint conditions with weight relation.On this basis,it is proved that any weight can be expressed by the set of extreme points of linear programming,and it is revealed that ordinal weight is essentially a weighted linear combination of extreme points.Furthermore,aiming at the problem of insufficient robustness of weighting method,the partial order relation is constructed by using extreme points,and the robustness of weight ranking is enhanced by Hasse graph.The example analysis shows that although the ordinal weights are different,the similar analysis results can be obtained by combining with the partial order method.