The Pareto optimality is a widely used concept for the multicriteria decision-making problems. However, this concept has a significant drawback—the set of Pareto optimal alternatives usually is large. Correspondingly, the problem of choosing a specific Pareto optimal alternative for the decision implementation is arising. This study proposes a new approach to select an “appropriate” alternative from the set of Pareto optimal alternatives. The proposed approach is based on ranking-theory methods used for ranking participants in sports tournaments. In the framework of the proposed approach, we build a special score matrix for a given multicriteria problem, which allows the use of the mentioned ranking methods and to choose the corresponding best-ranked alternative from the Pareto set as a solution of the problem. The proposed approach is particularly useful when no decision-making authority is available, or when the relative importance of various criteria has not been evaluated previously. The proposed approach is tested on an example of a materials-selection problem for a sailboat mast.

中文翻译：

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解决多准则决策问题的排名理论方法

帕累托最优性是用于多准则决策问题的广泛使用的概念。但是，此概念有一个很大的缺点-帕累托最优选择集通常很大。相应地，出现了为决策实施选择特定的帕累托最优替代方案的问题。这项研究提出了一种新方法，可以从帕累托最优选择集中选择一个“合适的”选择。所提出的方法基于用于对体育比赛的参与者进行排名的排名理论方法。在提出的方法的框架中，我们为给定的多准则问题构建了一个特殊的分数矩阵，该矩阵允许使用提到的排名方法，并从帕累托集中选择相应的最佳排名替代方案作为问题的解决方案。当没有决策机构可用时，或者以前没有评估过各种标准的相对重要性时，建议的方法特别有用。以帆船桅杆的材料选择问题为例对提出的方法进行了测试。