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On counting and constructing all admissible orders of the non-empty intervals in any finite chain

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Autor(es):
Sussner, Peter ; Vicentin, Felipe Scherer
Número total de Autores: 2
Tipo de documento: Artigo Científico
Fonte: FUZZY SETS AND SYSTEMS; v. 511, p. 9-pg., 2025-07-01.
Resumo

In many fields, there is a need to process data that only includes a finite number of values. To express the uncertainty regarding these values, one can use non-empty intervals, called epistemic, that are usually ordered in terms of the product, aka marginal, order. However, a partial order of this form is often insufficient in applications such as decision making, optimization, image segmentation, and edge detection. To this end, the given partial order of the non-empty intervals in a finite chain must be extended to a linear order, known as an admissible order. In this paper, we determine the number of all of these linear extensions and present an algorithm for generating them. (AU)

Processo FAPESP: 23/03449-0 - Investigações sobre a Construção e o Número das Extensões Lineares da Ordem Marginal na Classe dos Subintervalos de Qualquer Cadeia Finita
Beneficiário:Felipe Scherer Vicentin
Modalidade de apoio: Bolsas no Brasil - Iniciação Científica
Processo FAPESP: 20/09838-0 - BI0S - Brazilian Institute of Data Science
Beneficiário:João Marcos Travassos Romano
Modalidade de apoio: Auxílio à Pesquisa - Programa Centros de Pesquisa em Engenharia