Extremal values-based aggregation functions

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dc.contributor.authorHalaš, Radomír
dc.contributor.authorMesiar, Radko
dc.contributor.authorKolesárová, Anna
dc.contributor.authorSaadati, Reza
dc.contributor.authorHerrera, Francisco
dc.contributor.authorRodríguez Martínez, Iosu
dc.contributor.authorBustince Sola, Humberto
dc.contributor.departmentEstadística, Informática y Matemáticases_ES
dc.contributor.departmentEstatistika, Informatika eta Matematikaeu
dc.contributor.departmentInstitute of Smart Cities - ISCen
dc.date.accessioned2024-10-31T14:23:13Z
dc.date.issued2024-10-01
dc.date.updated2024-10-31T14:02:47Z
dc.description.abstractWe introduce and study aggregation functions based on extremal values, namely extended (𝑙, 𝑢)- aggregation functions whose outputs only depend on a fixed number 𝑙 of extremal lower input values and a fixed number 𝑢 of extremal upper input values, independently of the arity of the input 𝑛-tuples (𝑛 ≥ 𝑙 + 𝑢). We discuss several general properties of (𝑙, 𝑢)-aggregation functions and we study special (𝑙, 𝑢)-aggregation functions with neutral element, including t-conorms, t-norms and uninorms. We also study (𝑙, 𝑢)-aggregation functions defined by means of integrals with respect to discrete fuzzy measures, as well as (𝑙, 𝑢)-ordered weighted quasi-arithmetic means based on appropriate weighting vectors. We also stress some generalizations based on recently introduced new types of monotonicity. Some possible applications are sketched, too.en
dc.description.sponsorshipI. Rodriguez-Martinez and H. Bustince gratefully acknowledge the financial support of the Spanish Ministry of Science, project PID2022-136627NB-I00 financed by MCIN/AEI/10.13039/501100011033/FEDER, UE. R. Mesiar and A. Kolesarová are supported by the grant VEGA 1/0036/23. F. Herrera is financially supported by grant P18-FR4961. I. Rodriguez-Martinez is also partially supported by Tracasa Instrumental (iTRACASA) and Gobierno de Navarra - Departamento de Universidad, Innovación y Transformación Digital. R. Halaš was supported by the IGA grant of Palacký University Olomouc IGAPrF2024011.
dc.embargo.lift2026-10-01
dc.embargo.terms2026-10-01
dc.format.mimetypeapplication/pdfen
dc.identifier.citationHalas, R., Mesiar, R., Kolesárová, A., Saadati, R., Herrera, F., Rodriguez-Martinez, I., Bustince, H. (2024) Extremal values-based aggregation functions. Fuzzy Sets and Systems, 493-494, 1-16. https://doi.org/10.1016/j.fss.2024.109097.
dc.identifier.doi10.1016/j.fss.2024.109097
dc.identifier.issn0165-0114
dc.identifier.urihttps://academica-e.unavarra.es/handle/2454/52419
dc.language.isoeng
dc.publisherElsevier
dc.relation.ispartofFuzzy Sets and Systems 493–494, 2024, 109097
dc.relation.projectIDinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2022-136627NB-I00/ES/
dc.relation.projectIDinfo:eu-repo/grantAgreement/Gobierno de Navarra///
dc.relation.publisherversionhttps://doi.org/10.1016/j.fss.2024.109097
dc.rights© 2024 Elsevier B.V. This manuscript version is made available under the CC-BY-NC-ND 4.0.
dc.rights.accessRightsinfo:eu-repo/semantics/embargoedAccess
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subjectAggregation functionen
dc.subjectChoquet integralen
dc.subjectClassificationen
dc.subjectExtended aggregation functionen
dc.subjectOrdered weighted quasi-arithmetic meanen
dc.subjectSugeno integralen
dc.subjectSymmetric discrete fuzzy measureen
dc.subjectt-conormen
dc.subjectt-normen
dc.titleExtremal values-based aggregation functionsen
dc.typeinfo:eu-repo/semantics/article
dc.type.versioninfo:eu-repo/semantics/acceptedVersion
dspace.entity.typePublication
relation.isAuthorOfPublication70c54ba9-626d-461e-aa8a-a3f99f35ba13
relation.isAuthorOfPublication1bdd7a0e-704f-48e5-8d27-4486444f82c9
relation.isAuthorOfPublication.latestForDiscovery70c54ba9-626d-461e-aa8a-a3f99f35ba13

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