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Crisp dimension theory and valued preference relations. (English) Zbl 1048.91035
The referred paper contributes to the existing knowledge on the representation of binary preferences in real space. The main attention is focused on the problem of the adequate representation of valued (i.e., not crisp) preferences. After the introduction of the necessary concepts and racapitulation of classical results regarding the crisp preference, the concept of dimension function based upon a general representation for alpha-cuts is analyzed and the main results of the paper are derived. They regard the association of dimension functions to valued preference relations and the properties of those functions. Special attention is given to the computational complexity of the presented methods. The topics for eventual further research related to the presented theory are briefly recollected in the conclusions.

MSC:
91B06 Decision theory
03E72 Theory of fuzzy sets, etc.
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