Searching for the dimension of valued preference relations
The more information a preference structure gives, the more sophisticated representation techniques are necessary, so decision makers can have a global view of data and therefore a comprehensive understanding of the problem they are faced with. In this paper we propose to explore valued preference r...
| Authors: | ; ; ; |
|---|---|
| Format: | Article |
| Publication date: | 2003 |
| Country: | España |
| Institution: | Universidad Complutense de Madrid (UCM) |
| Repository: | Docta Complutense |
| Language: | English |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/57598 |
| Online Access: | https://hdl.handle.net/20.500.14352/57598 |
| Access Level: | Open access |
| Keyword: | 004.8 Multicriteria decision analysis Valued relations Dimension theory Inteligencia artificial (Informática) 1203.04 Inteligencia Artificial |
| _version_ | 1878731820994920449 |
|---|---|
| author | González Pachón, J. |
| author2 | Gómez González, Daniel Montero De Juan, Francisco Javier Yáñez Gestoso, Francisco Javier |
| author2_role | author author author |
| author_browse | González Pachón, J. Gómez González, Daniel Montero De Juan, Francisco Javier Yáñez Gestoso, Francisco Javier |
| author_facet | González Pachón, J. Gómez González, Daniel Montero De Juan, Francisco Javier Yáñez Gestoso, Francisco Javier |
| author_role | author |
| collection | Docta Complutense |
| description | The more information a preference structure gives, the more sophisticated representation techniques are necessary, so decision makers can have a global view of data and therefore a comprehensive understanding of the problem they are faced with. In this paper we propose to explore valued preference relations by means of a search for the number of underlying criteria allowing its representation in real space. A general representation theorem for arbitrary crisp binary relations is obtained, showing the difference in representation between incomparability-related to the intersection operator-and other inconsistencies-related to the union operator. A new concept of dimension is therefore proposed, taking into account inconsistencies in source of information. Such a result is then applied to each alpha-cut of valued preference relations. (C) 2002 Elsevier Science Inc. All rights reserved. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ES_3741e6e5d7eef2d4acf08fc3d1ccbba3 |
| institution | Universidad Complutense de Madrid (UCM) |
| instname_str | Universidad Complutense de Madrid (UCM) |
| language | eng |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:docta.ucm.es:20.500.14352/57598 |
| publishDate | 2003 |
| publishDateSort | 2003 |
| publisher | Elsevier Science INC |
| publisherStr | Elsevier Science INC |
| reponame_str | Docta Complutense |
| spelling | Searching for the dimension of valued preference relations González Pachón, J. Gómez González, Daniel Montero De Juan, Francisco Javier Yáñez Gestoso, Francisco Javier 004.8 Multicriteria decision analysis Valued relations Dimension theory Inteligencia artificial (Informática) 1203.04 Inteligencia Artificial The more information a preference structure gives, the more sophisticated representation techniques are necessary, so decision makers can have a global view of data and therefore a comprehensive understanding of the problem they are faced with. In this paper we propose to explore valued preference relations by means of a search for the number of underlying criteria allowing its representation in real space. A general representation theorem for arbitrary crisp binary relations is obtained, showing the difference in representation between incomparability-related to the intersection operator-and other inconsistencies-related to the union operator. A new concept of dimension is therefore proposed, taking into account inconsistencies in source of information. Such a result is then applied to each alpha-cut of valued preference relations. (C) 2002 Elsevier Science Inc. All rights reserved. Elsevier Science INC https://hdl.handle.net/20.500.14352/57598 |
| spellingShingle | Searching for the dimension of valued preference relations González Pachón, J. 004.8 Multicriteria decision analysis Valued relations Dimension theory Inteligencia artificial (Informática) 1203.04 Inteligencia Artificial |
| title | Searching for the dimension of valued preference relations |
| title_full | Searching for the dimension of valued preference relations |
| title_fullStr | Searching for the dimension of valued preference relations |
| title_full_unstemmed | Searching for the dimension of valued preference relations |
| title_short | Searching for the dimension of valued preference relations |
| title_sort | Searching for the dimension of valued preference relations |
| topic | 004.8 Multicriteria decision analysis Valued relations Dimension theory Inteligencia artificial (Informática) 1203.04 Inteligencia Artificial |
| topic_facet | 004.8 Multicriteria decision analysis Valued relations Dimension theory Inteligencia artificial (Informática) 1203.04 Inteligencia Artificial |
| url | https://hdl.handle.net/20.500.14352/57598 |