Searching for the dimension of valued preference relations

✍ Scribed by J. González-Pachón; D. Gómez; J. Montero; J. Yáñez

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 209 KB
• Volume: 33
• Category: Article
• ISSN: 0888-613X
• DOI: 10.1016/s0888-613x(02)00150-0

✦ Synopsis

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 a-cut of valued preference relations.