A Systematic Approach to Creating Fuzzy Region Objects from Real Spatial Data Sets

Fuzzy set theory has found increasing interest in the geosciences, geographic information systems, and spatial database systems to represent objects in the two-dimensional space that are afflicted with spatial fuzziness. From a system perspective, fuzzy spatial data types for fuzzy points, fuzzy lines, and fuzzy regions have been introduced, e.g., by the authors' formal Fuzzy Spatial Algebra (FUSA). The authors' Spatial Plateau Algebra (SPA) provides an implementation of FUSA by means of spatial plateau data types for plateau point, plateau line, and plateau region objects. It is based on well known non-fuzzy, crisp spatial data types. In this paper, we deal with the issue of constructing fuzzy region objects as plateau region objects from real point sets by leveraging domain expert knowledge and by assuming that each point is assigned a numerical value of a given application context. For this, we propose a general two-stage data extraction method. The first stage deploys a fuzzification policy to assign membership degrees to the points in the set. Examples of such policies are the execution of fuzzy clustering algorithms or the usage of fuzzy sets. The second stage uses a construction policy to build plateau regions by using the membership degrees generated in the first stage as input. Examples of such construction policies are the computation of fuzzy Voronoi diagrams or fuzzy Delaunay triangulations, or the calculation of fuzzy convex hulls.