Two models for comparing decisional maps. (1st January 2013) - Metchebon T., S. Aimé; Brison, Valérie; Pirlot, Marc
Among the many interesting decision problems raised by the use of geographic information systems, we address that of comparing maps representing the state of a given region at different stages of an evolution. We assume that the maps representing the state of the region are all partitioned in the same system of zones. Each zone is assessed on a discrete ordinal scale; the state of the region is described by the assessment of its zones. We analyse two models of preference on a set of maps of a region. The first only takes into account the frequency distribution of the zones of the region that belong to the various categories of the ordinal assessment scale. This model is a direct transposition of the expected utility model in decision under risk. Our second model takes into account not only the distribution of the zones but also one aspect related to their geographic location, namely the contiguity of the zones belonging to the same category. For both models, we develop procedures for eliciting the model's parameters and illustrate them on an example taken from a real world application.