Uncertain dominance degree: a new decision criterion under uncertainty theory

Many real-world decision problems involve ranking multiple candidates. In this context, uncertain dominance offers an alternative decision criterion within the framework of uncertainty theory. However, despite its many advantages, the dominance criterion fails to rank uncertain variables in some cases. In response to this, we define an uncertain dominance degree to quantify the extent to which one uncertain variable dominates another and propose a new decision criterion based on this measure, which enables a complete ranking of uncertain variables. In order to calculate the dominance degree, a benchmark variable needs to be set in advance, and we prove the existence of such a benchmark variable. Several theoretical properties of the proposed dominance degree are analysed to support its effectiveness in decision analysis. Moreover, we prove that our new criterion preserves the dominance relationship if the uncertain variables can be ranked by the dominance criterion and show the advantages of the new criterion over the dominance criterion. Finally, the proposed dominance degree is applied to portfolio selection to illustrate its applicability and practical relevance in real-world decision problem.