On the Construction of Admissible Orders for Tuples and Its Application to Imprecise Risk Matrices

The imprecision inherent in human opinions is not properly modeled by crisp numbers. Other more complex structures like intervals or tuples capture better the imprecision of human assessments. This makes them very useful in decision problems. However, they cannot be easily compared. Despite they grasp better decision-makers inaccuracy, the lack of a natural total order for such structures makes the determination of the best alternative a difficult task. In this contribution, we explore how to obtain new total orders for (ordered) tuples paying special attention to admissible orders (total orders that extend the lattice order). The resulting orders are applied to four-dimensional ordered tuples that represent risk assessments in an imprecise environment. In addition, two case studies involving risk matrices in educational transport and the construction of a metro station are also provided.