On the relationship between ordering measures, statistical preference, and the Xu and Yager order

S. S. Fernández, A. Bouchet, S. Díaz Vázquez, S. Montes

The utilization of intervals to model responses is a prevalent approach in contexts characterized by uncertainty. Consequently, the availability of procedures for the comparison of intervals assumes paramount importance in decisionmaking processes. In this work, we propose carrying out such a comparison using ordering measures for the lattice order, which provide an indicator of the degree to which one interval is smaller than another. By employing these axiomatically defined measures, we can obtain refinements of the lattice order.
In particular, we explore the relationship between ordering measures for intervals and the probabilistic relation that characterizes statistical preference in the case of continuous uniform random variables. Finally, we analyze the connection between the Xu and Yager order, which compares intervals by considering both endpoints, and the ordering measures obtained from the degree of statistical preference for these random variables.

Keywords: Intervals, ordering, statistical preference, measure

Multicriteria Decision Analysis I
June 10, 2025  3:30 PM
Auditorio 1. Ricard Vinyes

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