Partial orderings for hesitant fuzzy sets

New partial orderings =o=o, =p=p and =H=H are defined, studied and compared on the set HH of finite subsets of the unit interval with special emphasis on the last one. Since comparing two sets of the same cardinality is a simple issue, the idea for comparing two sets A and B of different cardinaliti...

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Autores: Garmendia Salvador, Luis, González del Campo, Ramón, Recasens Ferrés, Jorge|||0000-0003-2304-0032
Formato: artículo
Fecha de publicación:2017
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/104362
Acesso em linha:https://hdl.handle.net/2117/104362
https://dx.doi.org/10.1016/j.ijar.2017.02.008
Access Level:acceso abierto
Palavra-chave:Fuzzy logic
Hesitant fuzzy sets
Finite subsets of the unit interval
Partial ordering
T-norm
Fuzzy conjunction
Lògica difusa
Àrees temàtiques de la UPC::Matemàtiques i estadística::Lògica matemàtica
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spelling Partial orderings for hesitant fuzzy setsGarmendia Salvador, LuisGonzález del Campo, RamónRecasens Ferrés, Jorge|||0000-0003-2304-0032Fuzzy logicHesitant fuzzy setsFinite subsets of the unit intervalPartial orderingT-normFuzzy conjunctionLògica difusaÀrees temàtiques de la UPC::Matemàtiques i estadística::Lògica matemàticaNew partial orderings =o=o, =p=p and =H=H are defined, studied and compared on the set HH of finite subsets of the unit interval with special emphasis on the last one. Since comparing two sets of the same cardinality is a simple issue, the idea for comparing two sets A and B of different cardinalities n and m respectively using =H=H is repeating their elements in order to obtain two series with the same length. If lcm(n,m)lcm(n,m) is the least common multiple of n and m we can repeat every element of A lcm(n,m)/mlcm(n,m)/m times and every element of B lcm(n,m)/nlcm(n,m)/n times to obtain such series and compare them (Definition 2.2). (H,=H)(H,=H) is a bounded partially ordered set but not a lattice. Nevertheless, it will be shown that some interesting subsets of (H,=H)(H,=H) have a lattice structure. Moreover in the set BB of finite bags or multisets (i.e. allowing repetition of objects) of the unit interval a preorder =B=B can be defined in a similar way as =H=H in HH and considering the quotient set View the MathML sourceB¿=B/~ of BB by the equivalence relation ~ defined by A~BA~B when A=BBA=BB and B=BAB=BA, View the MathML source(B¿,=B) is a lattice and (H,=H)(H,=H) can be naturally embedded into it.Peer Reviewed20172017-05-0120172017-05-12journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/104362https://dx.doi.org/10.1016/j.ijar.2017.02.008reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 3.0 Spainhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/1043622026-05-27T15:37:01Z
dc.title.none.fl_str_mv Partial orderings for hesitant fuzzy sets
title Partial orderings for hesitant fuzzy sets
spellingShingle Partial orderings for hesitant fuzzy sets
Garmendia Salvador, Luis
Fuzzy logic
Hesitant fuzzy sets
Finite subsets of the unit interval
Partial ordering
T-norm
Fuzzy conjunction
Lògica difusa
Àrees temàtiques de la UPC::Matemàtiques i estadística::Lògica matemàtica
title_short Partial orderings for hesitant fuzzy sets
title_full Partial orderings for hesitant fuzzy sets
title_fullStr Partial orderings for hesitant fuzzy sets
title_full_unstemmed Partial orderings for hesitant fuzzy sets
title_sort Partial orderings for hesitant fuzzy sets
dc.creator.none.fl_str_mv Garmendia Salvador, Luis
González del Campo, Ramón
Recasens Ferrés, Jorge|||0000-0003-2304-0032
author Garmendia Salvador, Luis
author_facet Garmendia Salvador, Luis
González del Campo, Ramón
Recasens Ferrés, Jorge|||0000-0003-2304-0032
author_role author
author2 González del Campo, Ramón
Recasens Ferrés, Jorge|||0000-0003-2304-0032
author2_role author
author
dc.subject.none.fl_str_mv Fuzzy logic
Hesitant fuzzy sets
Finite subsets of the unit interval
Partial ordering
T-norm
Fuzzy conjunction
Lògica difusa
Àrees temàtiques de la UPC::Matemàtiques i estadística::Lògica matemàtica
topic Fuzzy logic
Hesitant fuzzy sets
Finite subsets of the unit interval
Partial ordering
T-norm
Fuzzy conjunction
Lògica difusa
Àrees temàtiques de la UPC::Matemàtiques i estadística::Lògica matemàtica
description New partial orderings =o=o, =p=p and =H=H are defined, studied and compared on the set HH of finite subsets of the unit interval with special emphasis on the last one. Since comparing two sets of the same cardinality is a simple issue, the idea for comparing two sets A and B of different cardinalities n and m respectively using =H=H is repeating their elements in order to obtain two series with the same length. If lcm(n,m)lcm(n,m) is the least common multiple of n and m we can repeat every element of A lcm(n,m)/mlcm(n,m)/m times and every element of B lcm(n,m)/nlcm(n,m)/n times to obtain such series and compare them (Definition 2.2). (H,=H)(H,=H) is a bounded partially ordered set but not a lattice. Nevertheless, it will be shown that some interesting subsets of (H,=H)(H,=H) have a lattice structure. Moreover in the set BB of finite bags or multisets (i.e. allowing repetition of objects) of the unit interval a preorder =B=B can be defined in a similar way as =H=H in HH and considering the quotient set View the MathML sourceB¿=B/~ of BB by the equivalence relation ~ defined by A~BA~B when A=BBA=BB and B=BAB=BA, View the MathML source(B¿,=B) is a lattice and (H,=H)(H,=H) can be naturally embedded into it.
publishDate 2017
dc.date.none.fl_str_mv 2017
2017-05-01
2017
2017-05-12
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/104362
https://dx.doi.org/10.1016/j.ijar.2017.02.008
url https://hdl.handle.net/2117/104362
https://dx.doi.org/10.1016/j.ijar.2017.02.008
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301629

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