Density based fuzzy membership functions in the context of geocomputation

Geocomputation has a long tradition in dealing with fuzzyness in different contexts, most notably in the challenges created by the representation of geographic space in digital form. Geocomputation tools should be able to address the imminent continuous nature of geo phenomena, and its accompanying fuzzyness. Fuzzy Set Theory allows partial memberships of entities to concepts with non-crisp boundaries. In general, the application of fuzzy methods is distance-based and for that reason is insensible to changes in density. In this paper a new method for defining density-based fuzzy membership functions is proposed. The method automatically determines fuzzy membership coefficients based on the distribution density of data. The density estimation is done using a Self-Organizing Map (SOM). The proposed method can be used to accurately describe clusters of data which are not well characterized using distance methods. We show the advantage of the proposed method over traditional distance-based membership functions.