On a total order on the set of Z-numbers based on discrete fuzzy numbers
| dc.contributor.author | Mir Fuentes, Arnau | |
| dc.contributor.author | Miguel Turullols, Laura de | |
| dc.contributor.author | Massanet, Sebastia | |
| dc.contributor.author | Mir Torres, Arnau | |
| dc.contributor.author | Riera, Juan Vicente | |
| dc.contributor.department | Estadística, Informática y Matemáticas | es_ES |
| dc.contributor.department | Estatistika, Informatika eta Matematika | eu |
| dc.date.accessioned | 2024-10-22T15:38:58Z | |
| dc.date.available | 2024-10-22T15:38:58Z | |
| dc.date.issued | 2024-07-02 | |
| dc.date.updated | 2024-10-22T15:17:48Z | |
| dc.description.abstract | Z-numbers were introduced by Zadeh in 2011 as a pair of fuzzy numbers (A, B), where A is interpreted as a fuzzy restriction on the values of a variable, while B is interpreted as a measure of certainty or sureness of A. From the initial proposal, several other approaches have been introduced in order to reduce the computational cost of the involved operations. One of such approaches is called discrete Z-numbers where A and B are modelled as discrete fuzzy numbers. In this paper, the construction of total orders on the set of discrete Z-numbers is investigated for the first time. Specifically, the total order is designed for discrete Z-numbers where the second component has membership values belonging to a finite and prefixed set of values. The method relies on solid and coherent linguistic criteria and several linguistic properties are analyzed. The order involves the transformation of the first components of the discrete Z-numbers by using the credibility of the second components in the sense that a lower credibility enlarges in a greater extent the uncertainty of the first component. Then a total order on the set of discrete fuzzy numbers is applied. Finally, a practical example on how to order discrete Z-numbers is presented and a comparison with other ranking methods is performed from which the strengths of our method are stressed. | en |
| dc.description.sponsorship | This work was partially supported by the R+D+i Project PID2020-113870GB-I00 'Desarrollo de herramientas de Soft Computing para la Ayuda al Diagnóstico Clínico y a la Gestión de Emergencias (HESOCODICE)', funded by MCIN/AEI/10.13039/501100011033/ and by the R+D+i Project PID2019-108392GB-I00 'Fusión de datos considerando las disimilitudes y otro tipo de relaciones entre los mismos y aplicación a inteligencia artificial' funded by MCIN/AEI/10.13039/501100011033/. Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. | |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.citation | Mir-Fuentes, A., De Miguel, L., Massanet, S., Mir, A., Riera, J. V. (2024) On a total order on the set of Z-numbers based on discrete fuzzy numbers. Computational and Applied Mathematics, 43(5), 1-27. https://doi.org/10.1007/s40314-024-02803-6. | |
| dc.identifier.doi | 10.1007/s40314-024-02803-6 | |
| dc.identifier.issn | 2238-3603 | |
| dc.identifier.uri | https://academica-e.unavarra.es/handle/2454/52354 | |
| dc.language.iso | eng | |
| dc.publisher | Springer | |
| dc.relation.ispartof | Computational and Applied Mathematics 43, 311, (2024) | |
| dc.relation.projectID | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-113870GB-I00/ES/ | |
| dc.relation.projectID | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-108392GB-I00/ES/ | |
| dc.relation.publisherversion | https://doi.org/10.1007/s40314-024-02803-6 | |
| dc.rights | © The Author(s) 2024. This article is licensed under a Creative Commons Attribution 4.0 International License. | |
| dc.rights.accessRights | info:eu-repo/semantics/openAccess | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.subject | Discrete fuzzy numbers | en |
| dc.subject | Discrete Z-numbers | en |
| dc.subject | Total order | en |
| dc.subject | Z-numbers | en |
| dc.title | On a total order on the set of Z-numbers based on discrete fuzzy numbers | en |
| dc.type | info:eu-repo/semantics/article | |
| dc.type.version | info:eu-repo/semantics/publishedVersion | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | b6673ff1-b94d-4852-be93-90b30a9c8555 | |
| relation.isAuthorOfPublication.latestForDiscovery | b6673ff1-b94d-4852-be93-90b30a9c8555 |