General admissibly ordered interval-valued overlap functions

Autor: Asmus, Tiago, Pereira Dimuro, Graçaliz, Sanz Delgado, José Antonio, Wieczynski, Jonata, Lucca, Giancarlo, Bustince Sola, Humberto
Přispěvatelé: Universidad Pública de Navarra. Departamento de Estadística, Informática y Matemáticas, Nafarroako Unibertsitate Publikoa. Estatistika, Informatika eta Matematikak Saila, Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
Jazyk: angličtina
Rok vydání: 2021
Předmět:
Zdroj: Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
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Popis: Overlap functions are a class of aggregation functions that measure the verlapping degree between two values. They have been successfully applied in several problems in which associativity is not required, such as classification and image processing. Some generalizations of overlap functions were proposed for them to be applied in problems with more than two classes, such as 𝑛- dimensional and general overlap functions. To measure the overlapping of interval data, interval-valued overlap functions were defined, and, later, they were also generalized in the form of 𝑛-dimensional and general interval-valued overlap functions. In order to apply some of those concepts in problems with interval data considering the use of admissible orders, which are total orders that refine the most used partial order for intervals, 𝑛-dimensional admissibly ordered interval-valued overlap functions were recently introduced, proving to be suitable to be applied in classification problems. However, the sole construction method presented for this kind of function do not allow the use of the well known lexicographical orders. So, in this work we combine previous developments to introduce general admissibly ordered interval-valued overlap functions, while also presenting different construction methods and the possibility to combine such methods, showcasing the flexibility and adaptability of this approach, while also being compatible with the lexicographical orders. Supported by the Spanish Ministry of Science and Technology (PC093-094 TFIPDL, TIN2016-81731-REDT, TIN2016-77356-P (AEI/FEDER, UE)), Spanish Ministry of Economy and Competitiveness through the Spanish National Research (project PID2019-108392GB-I00 / AEI / 10.13039/501100011033), UPNA (PJUPNA1926), CNPq (311429/2020-3, 301618/2019-4) and FAPERGS (19/2551-0001660).
Databáze: OpenAIRE
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