This paper deals with the construction of fuzzy costs and more particularly with their meaning in traffic assignment models based on fuzzy logic tools. The idea is to separate different possible semantics, namely imprecision, uncertainty and grade of preference. The classically encountered approach is based on the gathering of those different meanings into a single fuzzy cost. It is demonstrated in this paper that it may sometimes lead to inconsistencies. We propose another approach, based on decision theory with possibility measurement of uncertainty. (c) 2005 Elsevier Ltd. All rights reserved.