关键词: 多属性决策, 占优关系, 排序区间, 方案排序概率

Abstract: 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=(p_ij)_m×m, which shows how much degree that other alternatives dominated by a given alternative in pairwise comparisons; (ii) ranking interval denoted by RI(X_k)=[l_k^min,l_k^max], which indicates the best and worst rankings that an alternative can obtain relative to others; (iii) rank-order probability denoted by p(Υ_k), 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.

Key words: multiple attribute decision making, dominance relation, ranking interval, rank-order possibility