Ordering measures for interval-valued data through probabilistic comparison

S. Suarez-Fernandez, A. Bouchet, M. R. Oliveira, S. Montes, S. Diaz-Vazquez

Intervals provide a natural framework for representing information in contexts where imprecision and uncertainty arise. In this setting, it is essential to develop criteria to compare interval-valued data.

In this work, we introduce ordering measures for intervals as an extension of the lattice order. These measures assign values in [0,1] that quantify the degree to which one interval can be considered smaller than another.

The proposed measures are constructed via a probabilistic approach, associating each interval with a random variable and comparing the corresponding induced distributions.

This framework enables the comparison of arbitrary pairs of intervals and overcomes the dichotomous nature of the lattice order. We show that the proposed measures are consistent with the lattice order and induce total orders that preserve its structure.

Keywords: interval, ordering, random variable, lattice order

Statistical Models
September 4, 2026  9:00 AM
Aula 24

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