Systems of ordinal fuzzy logic with application to preference modelling

In this paper, we survey several many-valued propositional logics in which the truth-functions (in the real unit interval [0,1]) of their connectives are definable only from the natural ordering of the scale, without using an y richer algebraic structure. In particular we describe a complete notion o f proof for weighted formulas of the implication-free fragment of Godel log ic with involution. The usefulness of this logical framework for the formal ization of ordinal preference modelling is also shown. (C) 2001 Elsevier Sc ience B.V. All rights reserved.