Qualitative transformations in orders of magnitude spaces

The treatment of qualitative information and the study of how it is transformed from one situation to another are crucial to improve qualitative calculus results. Orders of magnitude algebras, based on finer discretizations than that given by the sign, provide a good frame for qualitative reasoning. The aim of this paper is to study how qualitative information given in orders of magnitude algebras is transformed, studying qualitative functions within this kind of structures, in such a way that their consistency with the real world of this kind of functions is ensured. This paper presents a characterization theorem of qualitative functions consistent with R.