Formalisms and Representations of Imperfect Geographic Objects

Abstract

This chapter first shows some examples of geographic data and spatial information to illustrate where and how imperfection takes shape. It then presents the main mathematical tools used to manipulate those two concepts, i.e. imperfection meant as partial knowledge and uncertainty meant as correspondence to reality, besides introducing the ways in which a geometric and topological object evolves. In the context of spatial analysis, it is often necessary to simultaneously combine attribute measures of a geographic object and geometric measures of the object through its adopted geometric model (vector or raster). Thus, it is necessary to introduce combination operators that imply membership or possibility distribution functions which characterize the imperfection of the fuzzy object. After recontextualizing the set operations defined over these fuzzy sets, the chapter also presents the mathematical functions that make it possible to define some set operations for keeping these membership properties.