Admissible orders for closed intervals of real numbers not based on the extremes of the intervals
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.
Authors
- Benjamín Bedregal (ORCID: https://orcid.org/0000-0002-6757-7934)
- Antonio Francisco Roldán López de Hierro (ORCID: https://orcid.org/0000-0002-6956-4328)
- Humberto Bustince (ORCID: https://orcid.org/0000-0002-1279-6195)
- Graçaliz Pereira Dimuro (ORCID: https://orcid.org/0000-0001-6986-9888)
- Susana Montes (ORCID: https://orcid.org/0000-0002-4701-2207)
- Javier Fernández (ORCID: https://orcid.org/0000-0003-4427-3935)
- Radko Mesiar
Institutions
- Slovak University of Technology in Bratislava (SK)
- Universidade Federal do Rio Grande (BR)
- Universidad de Oviedo (ES)
- Universidad de Granada (ES)
- Universidad Pública de Navarra (UPNA) (ES)
- University of Ostrava (CZ)
- Universidade Federal do Rio Grande do Norte (BR)
Publication Details
- Journal
- Fuzzy Sets and Systems
- Published
- 2025-09-30
- DOI
- https://doi.org/10.1016/j.fss.2025.109602
- Citations
- 1
- Primary Topic
- Numerical Methods and Algorithms
- Type
- article
- Field-Weighted Citation Impact
- 1.50
Funders
- European Commission
- Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
- Conselho Nacional de Desenvolvimento Científico e Tecnológico
- Fundação de Amparo à Pesquisa do Estado do Rio Grande do Sul
- Vedecká Grantová Agentúra MŠVVaŠ SR a SAV
- Universidad Pública de Navarra
- Junta de Andalucía
- Agencia Estatal de Investigación