On the dimension of fuzzy preference relations

The concept of Dimension plays a key role in the context of crisp (classical) preference modelling. Dimension analysis allows a better insight of structure of individual preferences, giving a hint about the complexity of the preference modelling problem. Several attempts can be found in the literature in order to translate such a concept and its associated procedures into fuzzy preference models. In this paper, we shallrst of all discuss some of these approaches, showing that no more extra knowledge about the problem is sometimes attained, mainly due to some a priori introduced restrictions. Then we shall propose an alternative approach based upon the analysis of all associated crisp ®-cuts. Some consequences in related fuzzy preference modelling problems are also discussed.