@misc{10481/107380,
year = {2026},
month = {1},
url = {https://hdl.handle.net/10481/107380},
abstract = {Due to its reasonable properties, the Kulisch and Miranker binary relation on the family of all
closed and bounded real intervals has attracted the attention of many researchers, especially in
the field of Computation. However, it is not total, so there are intervals that are not comparable.
To face this problem, Bustince et al. introduced the notion of admissible order, which is coherent to
the Kulisch and Miranker binary relation. Due to its technical construction, most of the examples
of admissible orders are defined by only employing the extremes of such intervals. In this paper
we introduce a non-countable family of admissible orders in the set of all closed and bounded
subintervals contained in a concrete closed and bounded real interval. The approach is novel in
two senses: on the one hand, due to the mathematical objects that are involved (a dense sequence
and a family of continuous functions); and, on the other hand, we do not handle the intervals
through their extremes, but only by their interior points.},
organization = {Consejería de Universidad, Investigación e Innovación, Junta de Andalucía – European Union, Program FEDER Andalucía 2021–2027 (project C-EXP-153-UGR23)},
organization = {National Council for Scientific and Technological Development (CNPq, projects 311429/2020-3, 304118/2023-0, 407206/2023-0)},
organization = {Coordination for the Improvement of Higher Education Personnel (CAPES, project Capes-Print 88887.917043/2023-00)},
organization = {Research Support Foundation of the State of Rio Grande do Sul (FAPERGS, project 23/2551-0001865-9)},
organization = {MCIN/AEI/10.13039/501100011033 – FEDER, EU (projects PID2022-139886NB-I00; PID2022-136627NB-I00)},
organization = {Universidad Pública de Navarra (Open access)},
publisher = {Elsevier},
keywords = {interval-valued fuzzy sets},
keywords = {Admissible order},
keywords = {Dense sequence},
title = {Admissible orders for closed intervals of real numbers not based on the extremes of the intervals},
doi = {10.1016/j.fss.2025.109602},
author = {Bustince, Humberto and Bedregal, Benjamín and Montes, Susana and Mesiar, Radko and Roldán López de Hierro, Antonio Francisco and Pereira Dimuro, Graçaliz and Fernández, Javier},
}