Abstract: In view of the partial order set method that can not solve the multi criteria decision problem which contains weight, this paper proposes a multi criteria decision making method with implicitly empowering weights. First it is expressed as a poset which contains n scheme and m criteria decision problem, then forms a new poset which containsm criterions according to the weight order. The poset relationships which contain each other prove that the new poset not only contains the weighted information, but also has a stronger ability of sorting. This way it only needs weight order without concrete weight in exercising, which is suitable for the multi criteria decision making problems whose weight is difficult to determine. This paper takes the Three Gorges reservoir water quality evaluation as an example, showing that the new method is superior to the original partial order set , and it can cluster and sort 13 schemes, but the original method is hardly applied to this example.

Key words: poset, multiple criteria decision making, weight, evaluation set

摘要： 针对偏序集方法不能解决含有权重的多准则决策问题,提出一种“隐式”赋权的偏序决策方法。首先将含有m个方案和n个准则的决策问题表示成偏序集,之后按权重由大到小的顺序,对准则进行逐步相加形成n个新的准则,得到一个新的偏序集。根据偏序集间的包含关系,证明了新偏序集不仅蕴含了权重信息,而且比初始偏序集有更强的排序能力。结果表明,该法在应用中仅需获取权重排序信息,无需精确权重,适用于权重难以确定的多准则决策问题。以三峡库区水质评价为例,例子表明新方法明显优于原有的偏序决策方法,能够对13个方案进行聚类和排序,而原有方法在该例中几乎难以应用。

关键词: 偏序集, 多准则决策, 权重, 评价集