在多属性决策问题中，不同的属性权重会产生不同的评价结果。由于实际问题的复杂性与不确定性，决策者对于属性权重的确定也存在不确定性。这些不确定既来自现实问题的复杂性和可变性，也来自决策者选择的模糊性与随机性。目前已有的研究主要是将不确定的权重信息转化为相对确定的信息（如转化为区间数等），硬性地消除了不确定，从而给决策结果带来较大风险。本文从方案排序的视角出发，研究在权重空间下，方案的占优关系和排序的稳健性。首先，定义了占优矩阵用于刻画不确定权重信息下方案两两比较的占优关系；其次，分析了方案的排序区间，即在所有可能存在的权重组合下，方案的最好排序和最差排序。然后，定义了方案的全排序排序概率，并且给出了排序概率的计算方法。进而，我们给出了方法的决策步骤和实施过程。最后，本文将该方法应用到某远洋集团的港口评估当中。
In multiple attribute decision analysis (MADA), reaching a consensus about exact weights may be difficult due to the complexity and uncertainty of actual problems. However, a number of existing weight computing methods are inadequate since they obtain different sets of exact weight values in terms of different kinds of preference or regulations. That is, it will result in some problems in the optimal alternative choice, ranking robustness or risk analysis. To address these problems, an approach about dominance relation and ranking stability analysis of alternatives is developed based on all feasible weights instead of determining a set of certain weights. Specifically, it is determined. (i) pairwise dominance matrix denoted by P=(pij)m×m, which shows how much degree that other alternatives dominated by a given alternative in pairwise comparisons; (ii) ranking interval denoted by RI(Xk)=[lkmin,lkmax], which indicates the best and worst rankings that an alternative can obtain relative to others; (iii) rank-order probability denoted by p(Υk), which reveals the stability of a given rank-order over all feasible weights. Finally, an example in Wu and Liang (2012) and a case study of ports evaluation are employed to illustrate the application of the proposed approach. From the result of Wu and Liang's example, it can be seen that the rank-order obtained by our approach is not the same as the literature. This is obviously caused by different treatment with uncertain weights. From the result of our case study, a final rank-order of the assessed ports is obtained: A5 > A1 > A2 > A3 > A4.
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