Pointed order polytopes: Studying geometrical aspects of the polytope of bi-capacities
| dc.contributor.author | Miranda Menéndez, Pedro | |
| dc.contributor.author | García Segador, Pedro | |
| dc.date.accessioned | 2023-06-16T14:25:38Z | |
| dc.date.available | 2023-06-16T14:25:38Z | |
| dc.date.issued | 2021-11-08 | |
| dc.description.abstract | In this paper we study some geometrical questions about the polytope of bi-capacities. For this, we introduce the concept of pointed order polytope, a natural generalization of order polytopes. Basically, a pointed order polytope is a polytope that takes advantage of the order relation of a partially ordered set and such that there is a relevant element in the structure. We study which are the set of vertices of pointed order polytopes and sort out a simple way to determine whether two vertices are adjacent. We also study the general form of its faces. Next, we show that the set of bi-capacities is a special case of pointed order polytope. Then, we apply the results obtained for general pointed order polytopes for bi-capacities, allowing to characterize vertices and adjacency, and obtaining a bound for the diameter of this important polytope arising in Multicriteria Decision Making. | |
| dc.description.department | Depto. de Estadística e Investigación Operativa | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Ministerio de Economía y Competitividad (España) | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/75934 | |
| dc.identifier.citation | Miranda P, García-Segador P. Pointed order polytopes: Studying geometrical aspects of the polytope of bi-capacities. Fuzzy Sets and Systems 2022; 444: 182–205. [DOI: 10.1016/j.fss.2021.11.001] | |
| dc.identifier.doi | 10.1016/j.fss.2021.11.001 | |
| dc.identifier.issn | 0165-0114 | |
| dc.identifier.officialurl | https://doi.org/10.1016/j.fss.2021.11.001 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/5003 | |
| dc.journal.title | Fuzzy Sets and Systems | |
| dc.language.iso | eng | |
| dc.page.final | 205 | |
| dc.page.initial | 182 | |
| dc.publisher | Elsevier Science Bv | |
| dc.relation.projectID | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-095194-B-I00/ES/ESTIMACION Y CONTRASTES DE HIPOTESIS ROBUSTOS PARA DATOS DE ALTA DIMENSION BASADOS EN LA DIVERGENCIA DE POTENCIAS DE DENSIDAD/ | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 512 | |
| dc.subject.keyword | Theory of computation | |
| dc.subject.keyword | Randomness | |
| dc.subject.keyword | geometry and discrete structures | |
| dc.subject.ucm | Geometría | |
| dc.subject.unesco | 1204 Geometría | |
| dc.title | Pointed order polytopes: Studying geometrical aspects of the polytope of bi-capacities | |
| dc.type | journal article | |
| dc.type.hasVersion | VOR | |
| dc.type.hasVersion | AM | |
| dc.volume.number | 444 | |
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