Abstract :
[en] In the field of land management, it is not uncommon to have a geographic map, representing a region under study, and divided into geographic units. Each unit is assessed on an ordinal scale describing its degree of suitability for some usage, for instance housing, or its state of degradation with respect to sustainable development criteria. We call such a map a decisional map. After a while, and for example, after the application of some policies aiming to improve the situation, the state of the units evolves. For some units, the state has improved, and for some others, it has deteriorated. What we want to know is whether the global state of the map has improved or not. The purpose of this work is to provide models to compare the state of a region at different stages of its evolution. We formulate three mathematical models all based on several axioms that make sense in some geographic contexts. We start with a simple one, which doesn't take into account any geographic aspect. In the second one, we introduce one geographic aspect and then we generalize this model to take into account any finite number of geographic aspects.
