Some problems on the definition of fussy preference relations
Fuzzy Sets and Systems
On strict preference relations
Fuzzy Sets and Systems - Special issue: Aggregation and best choices of imprecise opinions
Fuzzy Sets and Systems
Dimension of fuzzy ordered sets
Fuzzy Sets and Systems
Journal of Algorithms
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
On the relevance of some families of fuzzy sets
Fuzzy Sets and Systems
Accuracy statistics for judging soft classification
International Journal of Remote Sensing
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Classical dimension theory, when applied to preference modeling, is based upon the assumption that linear ordering is the only elemental notion for rationality. In fact, crisp preferences are in some way decomposed into basic criteria, each one being a linear order. In this paper, we propose that indeed dimension is relative to a previous idea of rationality, but such a rationality is not unique. In particular, we explore alternative approaches to dimension, based upon a more general representation and allowing different classes of orders for basic criteria. In this way, classical dimension theory is generalized. As a first consequence, we explore the existence of crisp preference representations not being based upon linear orders. As a second consequence, it is suggested that an analysis of valued preference relations can be developed in terms of the representations of all α-cuts.