Representation of quasi-overlap functions for normal convex fuzzy truth values based on generalized extended overlap functions

At present, (quasi-)overlap functions have been extended to various universes of discourse and become a hot research topic. Meanwhile, the investigation of extended aggregation operations for normal convex fuzzy truth values has also attracted much attention. This paper mainly studies the representa...

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Autores: Wang, Yiding, Qiao, Junsheng, Zhang, Wei, Bustince Sola, Humberto
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2025
País:España
Institución:Universidad Pública de Navarra
Repositorio:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
OAI Identifier:oai:academica-e.unavarra.es:2454/53393
Acceso en línea:https://hdl.handle.net/2454/53393
Access Level:acceso embargado
Palabra clave:Generalized extended overlap functions
Normal convex fuzzy truth values
Quasi-overlap functions
Type-2 fuzzy sets
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spelling Representation of quasi-overlap functions for normal convex fuzzy truth values based on generalized extended overlap functionsWang, YidingQiao, JunshengZhang, WeiBustince Sola, HumbertoGeneralized extended overlap functionsNormal convex fuzzy truth valuesQuasi-overlap functionsType-2 fuzzy setsAt present, (quasi-)overlap functions have been extended to various universes of discourse and become a hot research topic. Meanwhile, the investigation of extended aggregation operations for normal convex fuzzy truth values has also attracted much attention. This paper mainly studies the representation of quasi-overlap functions for normal convex fuzzy truth values based on generalized extended overlap functions, which is the fundamental problem in the whole study of overlap functions for normal convex fuzzy truth values. Firstly, we present the definitions of (restrictive-)quasi-overlap functions and lattice-ordered-(restrictive-)quasi-overlap functions for normal convex fuzzy truth values and generalized extended overlap functions, respectively. Secondly, we present the (equivalent) characterizations for the closure properties of generalized extended overlap functions for various fuzzy truth values. Thirdly, we characterize the basic properties of generalized extended overlap functions for normal convex fuzzy truth values. Finally, by an equivalent characterization with a prerequisite, we successfully represent quasi-overlap functions for normal convex fuzzy truth values based on generalized extended overlap functions. Notably, we can quickly obtain (restrictive-)quasi-overlap functions for normal convex fuzzy truth values using the left-continuous quasi-overlap functions on interval [0,1]. Moreover, regarding the relationships between four types of quasi-overlap functions for normal convex fuzzy truth values, the details implication relations are that lattice-ordered-(restrictive-)quasi-overlap functions are strictly stronger than (restrictive-)quasi-overlap functions for normal convex fuzzy truth values even if all of them are constructed by generalized extended overlap functions.Supported by National Natural Science Foundation of China (62166037, 12201512), Science and Technology Program of Gansu Province (20JR10RA101), Longyuan Youth Innovation and Entrepreneurship Talent Project (6017/20231004), Funds for Innovative Fundamental Research Group Project of Gansu Province (23JRRA684), research project PID2022-136627NB-I00, and MCIN/AEI/10.13039/501100011033/FEDER, UE.ElsevierEstadística, Informática y MatemáticasEstatistika, Informatika eta MatematikaInstitute of Smart Cities - ISC2025info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://hdl.handle.net/2454/53393reponame:Academica-e. Repositorio Institucional de la Universidad Pública de Navarrainstname:Universidad Pública de NavarraInglésinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2022-136627NB-I00© 2024 Elsevier Inc. This manuscript version is made available under the CC-BY-NC-ND 4.0https://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/embargoedAccessoai:academica-e.unavarra.es:2454/533932026-06-17T12:41:47Z
dc.title.none.fl_str_mv Representation of quasi-overlap functions for normal convex fuzzy truth values based on generalized extended overlap functions
title Representation of quasi-overlap functions for normal convex fuzzy truth values based on generalized extended overlap functions
spellingShingle Representation of quasi-overlap functions for normal convex fuzzy truth values based on generalized extended overlap functions
Wang, Yiding
Generalized extended overlap functions
Normal convex fuzzy truth values
Quasi-overlap functions
Type-2 fuzzy sets
title_short Representation of quasi-overlap functions for normal convex fuzzy truth values based on generalized extended overlap functions
title_full Representation of quasi-overlap functions for normal convex fuzzy truth values based on generalized extended overlap functions
title_fullStr Representation of quasi-overlap functions for normal convex fuzzy truth values based on generalized extended overlap functions
title_full_unstemmed Representation of quasi-overlap functions for normal convex fuzzy truth values based on generalized extended overlap functions
title_sort Representation of quasi-overlap functions for normal convex fuzzy truth values based on generalized extended overlap functions
dc.creator.none.fl_str_mv Wang, Yiding
Qiao, Junsheng
Zhang, Wei
Bustince Sola, Humberto
author Wang, Yiding
author_facet Wang, Yiding
Qiao, Junsheng
Zhang, Wei
Bustince Sola, Humberto
author_role author
author2 Qiao, Junsheng
Zhang, Wei
Bustince Sola, Humberto
author2_role author
author
author
dc.contributor.none.fl_str_mv Estadística, Informática y Matemáticas
Estatistika, Informatika eta Matematika
Institute of Smart Cities - ISC
dc.subject.none.fl_str_mv Generalized extended overlap functions
Normal convex fuzzy truth values
Quasi-overlap functions
Type-2 fuzzy sets
topic Generalized extended overlap functions
Normal convex fuzzy truth values
Quasi-overlap functions
Type-2 fuzzy sets
description At present, (quasi-)overlap functions have been extended to various universes of discourse and become a hot research topic. Meanwhile, the investigation of extended aggregation operations for normal convex fuzzy truth values has also attracted much attention. This paper mainly studies the representation of quasi-overlap functions for normal convex fuzzy truth values based on generalized extended overlap functions, which is the fundamental problem in the whole study of overlap functions for normal convex fuzzy truth values. Firstly, we present the definitions of (restrictive-)quasi-overlap functions and lattice-ordered-(restrictive-)quasi-overlap functions for normal convex fuzzy truth values and generalized extended overlap functions, respectively. Secondly, we present the (equivalent) characterizations for the closure properties of generalized extended overlap functions for various fuzzy truth values. Thirdly, we characterize the basic properties of generalized extended overlap functions for normal convex fuzzy truth values. Finally, by an equivalent characterization with a prerequisite, we successfully represent quasi-overlap functions for normal convex fuzzy truth values based on generalized extended overlap functions. Notably, we can quickly obtain (restrictive-)quasi-overlap functions for normal convex fuzzy truth values using the left-continuous quasi-overlap functions on interval [0,1]. Moreover, regarding the relationships between four types of quasi-overlap functions for normal convex fuzzy truth values, the details implication relations are that lattice-ordered-(restrictive-)quasi-overlap functions are strictly stronger than (restrictive-)quasi-overlap functions for normal convex fuzzy truth values even if all of them are constructed by generalized extended overlap functions.
publishDate 2025
dc.date.none.fl_str_mv 2025
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2454/53393
url https://hdl.handle.net/2454/53393
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2022-136627NB-I00
dc.rights.none.fl_str_mv © 2024 Elsevier Inc. This manuscript version is made available under the CC-BY-NC-ND 4.0
https://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/embargoedAccess
rights_invalid_str_mv © 2024 Elsevier Inc. This manuscript version is made available under the CC-BY-NC-ND 4.0
https://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv embargoedAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
instname:Universidad Pública de Navarra
instname_str Universidad Pública de Navarra
reponame_str Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
collection Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
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repository.mail.fl_str_mv
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