Study on the expression of admissible orders from a lexicographic order

E. Torres Manzanera, S. Díaz Vázquez, S. Montes

Intervals have been extensively used as substitutes for precise values in situations where assessments are subject to imprecision, thereby enabling the representation of uncertainty that cannot be captured by single-point evaluations.
However, their formal study is more intricate, particularly concerning ordering. A universally accepted total order exists for numbers, but this is not the case for intervals. The most intuitive order among intervals, the lattice order, is not total.
Admissible orders have been a subject of significant interest in the literature, as they are both total and coincide with the lattice order when the latter does not lead to incomparability. A key question that has emerged is whether admissible orders can be expressed as a type of lexicographic order. In this contribution, we recover an admissible
order that is a (just) one-component lexicographic order and detail its main properties. This order is based on the interleaving function.

Keywords: interval ordering, admissible order, lexicographic order

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