Areas of fuzzy geographical entities

The use of geographical entities with fuzzy spatial extent, called here fuzzy geographical entities (FGE’s), in Geographical Information Systems requires the existence of operators capable of processing them. This paper focuses on the computation of areas of FGE’s. Two methods are considered, one crisp due to Rosenfeld (1984), which will be shown to be limited in its applicability, and the other fuzzy that is a new approach. The new fuzzy area operator gives more information about the possible values of the area and enables the propagation of the fuzziness in the spatial extent of the entity. Crisp and fuzzy areas have different meanings and the use of one or the other depends not only on the purpose of the computation but also on the semantics of the membership functions. Since the fuzzy area operator generates fuzzy numbers when the FGE’s are represented by normal fuzzy sets, arithmetic operations can be performed with these areas using fuzzy arithmetic. However, as will be shown, care must be taken when using the arithmetic operators because in some situations the usual fuzzy operators shouldn’t be applied. Properties of the fuzzy area operators are analyzed, establishing a parallel with properties of the areas of crisp sets.