On the Conditions for Total Orderings in Lexicographic Methods to Rank Fuzzy Numbers

descriptionPublicationkeyboard_double_arrow_right Article 26 Feb 2024 English Publisher:Springer Science and Business Media LLCJournal:International Journal of Fuzzy Systems, volume 26, pages 1,417-1,427 (issn: 1562-2479, eissn: 2199-3211,

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Authors: Salas Molina, Francisco; Pla Santamaría, David; García Bernabeu, Ana María; Reig-Mullor, Javier;

doi: 10.1007/s40815-023-01676-x

On the Conditions for Total Orderings in Lexicographic Methods to Rank Fuzzy Numbers

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Abstract

Abstract Lexicographic methods to rank fuzzy numbers present the advantages of simplicity, consistency with human intuition, and power of discrimination. In this paper, we tackle the problem of finding the conditions for these methods to produce a rank in specific steps. Our main results are twofold. First, we prove that a necessary and sufficient condition for a ranking function to be a total order is that this function is either injective, surjective, or bijective. Second, we provide further insight into the required steps for a lexicographic order to rank same-type and different-type fuzzy numbers. A counterexample refutes a conjecture in the literature about the maximum number of steps needed to rank different-type fuzzy numbers.

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Lexicographic order, ECONOMIA APLICADA, Fuzzy numbers, 15.- Proteger, restaurar y promover la utilización sostenible de los ecosistemas terrestres, gestionar de manera sostenible los bosques, combatir la desertificación y detener y revertir la degradación de la tierra, y frenar la pérdida de diversidad biológica, 14.- Conservar y utilizar de forma sostenible los océanos, mares y recursos marinos para lograr el desarrollo sostenible, 08.- Fomentar el crecimiento económico sostenido, inclusivo y sostenible, el empleo pleno y productivo, y el trabajo decente para todos, 12.- Garantizar las pautas de consumo y de producción sostenibles, 16.- Promover sociedades pacíficas e inclusivas para el desarrollo sostenible, facilitar acceso a la justicia para todos y crear instituciones eficaces, responsables e inclusivas a todos los niveles, Total order, ECONOMIA FINANCIERA Y CONTABILIDAD, Ranking, 04.- Garantizar una educación de calidad inclusiva y equitativa, y promover las oportunidades de aprendizaje permanente para todos

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