A Generalization of Trapezoidal Fuzzy Numbers Based on Modal Interval Theory
We propose a generalization of trapezoidal fuzzy numbers based on modal interval theory, which we name 'modal interval trapezoidal fuzzy numbers'. In this generalization, we accept that the alpha cuts associated with a trapezoidal fuzzy number can be modal intervals, also allowing that two...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | Universidad de Barcelona |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/122232 |
| Acceso en línea: | https://hdl.handle.net/2445/122232 |
| Access Level: | acceso abierto |
| Palabra clave: | Sistemes borrosos Conjunts borrosos Anàlisi d'intervals (Matemàtica) Matemàtica Fuzzy systems Fuzzy sets Interval analysis (Mathematics) Mathematics |
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A Generalization of Trapezoidal Fuzzy Numbers Based on Modal Interval TheoryJorba, LambertAdillón, RománSistemes borrososConjunts borrososAnàlisi d'intervals (Matemàtica)MatemàticaFuzzy systemsFuzzy setsInterval analysis (Mathematics)MathematicsWe propose a generalization of trapezoidal fuzzy numbers based on modal interval theory, which we name 'modal interval trapezoidal fuzzy numbers'. In this generalization, we accept that the alpha cuts associated with a trapezoidal fuzzy number can be modal intervals, also allowing that two interval modalities can be associated with a trapezoidal fuzzy number. In this context, it is difficult to maintain the traditional graphic representation of trapezoidal fuzzy numbers and we must use the interval plane in order to represent our modal interval trapezoidal fuzzy numbers graphically. Using this representation, we can correctly reflect the modality of the alpha cuts. We define some concepts from modal interval analysis and we study some of the related properties and structures, proving, among other things, that the inclusion relation provides a lattice structure on this set. We will also provide a semantic interpretation deduced from the modal interval extensions of real continuous functions and the semantic modal interval theorem. The application of modal intervals in the field of fuzzy numbers also provides a new perspective on and new applications of fuzzy numbers.MDPI2017info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://hdl.handle.net/2445/122232Articles publicats en revistes (Matemàtica Econòmica, Financera i Actuarial)reponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglésReproducció del document publicat a: https://doi.org/10.3390/sym9100198Symmetry, 2017, vol. 9, num. 10(198), p. 1-20https://doi.org/10.3390/sym9100198cc-by (c) Jorba, Lambert et al., 2017http://creativecommons.org/licenses/by/3.0/esinfo:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/1222322026-05-27T06:46:51Z |
| dc.title.none.fl_str_mv |
A Generalization of Trapezoidal Fuzzy Numbers Based on Modal Interval Theory |
| title |
A Generalization of Trapezoidal Fuzzy Numbers Based on Modal Interval Theory |
| spellingShingle |
A Generalization of Trapezoidal Fuzzy Numbers Based on Modal Interval Theory Jorba, Lambert Sistemes borrosos Conjunts borrosos Anàlisi d'intervals (Matemàtica) Matemàtica Fuzzy systems Fuzzy sets Interval analysis (Mathematics) Mathematics |
| title_short |
A Generalization of Trapezoidal Fuzzy Numbers Based on Modal Interval Theory |
| title_full |
A Generalization of Trapezoidal Fuzzy Numbers Based on Modal Interval Theory |
| title_fullStr |
A Generalization of Trapezoidal Fuzzy Numbers Based on Modal Interval Theory |
| title_full_unstemmed |
A Generalization of Trapezoidal Fuzzy Numbers Based on Modal Interval Theory |
| title_sort |
A Generalization of Trapezoidal Fuzzy Numbers Based on Modal Interval Theory |
| dc.creator.none.fl_str_mv |
Jorba, Lambert Adillón, Román |
| author |
Jorba, Lambert |
| author_facet |
Jorba, Lambert Adillón, Román |
| author_role |
author |
| author2 |
Adillón, Román |
| author2_role |
author |
| dc.subject.none.fl_str_mv |
Sistemes borrosos Conjunts borrosos Anàlisi d'intervals (Matemàtica) Matemàtica Fuzzy systems Fuzzy sets Interval analysis (Mathematics) Mathematics |
| topic |
Sistemes borrosos Conjunts borrosos Anàlisi d'intervals (Matemàtica) Matemàtica Fuzzy systems Fuzzy sets Interval analysis (Mathematics) Mathematics |
| description |
We propose a generalization of trapezoidal fuzzy numbers based on modal interval theory, which we name 'modal interval trapezoidal fuzzy numbers'. In this generalization, we accept that the alpha cuts associated with a trapezoidal fuzzy number can be modal intervals, also allowing that two interval modalities can be associated with a trapezoidal fuzzy number. In this context, it is difficult to maintain the traditional graphic representation of trapezoidal fuzzy numbers and we must use the interval plane in order to represent our modal interval trapezoidal fuzzy numbers graphically. Using this representation, we can correctly reflect the modality of the alpha cuts. We define some concepts from modal interval analysis and we study some of the related properties and structures, proving, among other things, that the inclusion relation provides a lattice structure on this set. We will also provide a semantic interpretation deduced from the modal interval extensions of real continuous functions and the semantic modal interval theorem. The application of modal intervals in the field of fuzzy numbers also provides a new perspective on and new applications of fuzzy numbers. |
| publishDate |
2017 |
| dc.date.none.fl_str_mv |
2017 |
| dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
| format |
article |
| status_str |
publishedVersion |
| dc.identifier.none.fl_str_mv |
https://hdl.handle.net/2445/122232 |
| url |
https://hdl.handle.net/2445/122232 |
| dc.language.none.fl_str_mv |
Inglés |
| language_invalid_str_mv |
Inglés |
| dc.relation.none.fl_str_mv |
Reproducció del document publicat a: https://doi.org/10.3390/sym9100198 Symmetry, 2017, vol. 9, num. 10(198), p. 1-20 https://doi.org/10.3390/sym9100198 |
| dc.rights.none.fl_str_mv |
cc-by (c) Jorba, Lambert et al., 2017 http://creativecommons.org/licenses/by/3.0/es info:eu-repo/semantics/openAccess |
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cc-by (c) Jorba, Lambert et al., 2017 http://creativecommons.org/licenses/by/3.0/es |
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openAccess |
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application/pdf |
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MDPI |
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MDPI |
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Articles publicats en revistes (Matemàtica Econòmica, Financera i Actuarial) reponame:Dipòsit Digital de la UB instname:Universidad de Barcelona |
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Universidad de Barcelona |
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Dipòsit Digital de la UB |
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Dipòsit Digital de la UB |
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15,300724 |