%0 Journal Article
%A González Pachón, J.
%A Gómez González, Daniel
%A Montero De Juan, Francisco Javier
%A Yáñez Gestoso, Francisco Javier
%T Searching for the dimension of valued preference relations
%D 2003
%@ 0888-613X
%U https://hdl.handle.net/20.500.14352/57598
%X 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.
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