Plateau Regions: An Implementation Concept for Fuzzy Regions in Spatial Databases and GIS

Many geographical applications need to model spatial phenomena with vague or indeterminate boundaries and interiors. A popular paradigm adopted by the GIS community for this task at the modeling level is fuzzy set theory. A spatial object is fuzzy if locations exist that cannot be assigned completely to the object or to its complement. In previous work, we have proposed an abstract data model of fuzzy spatial data types for fuzzy points, fuzzy lines, and fuzzy regions to represent the indeterminacy of spatial data. This paper focuses on the problem of finding an appropriate implementation approach to fuzzy regions. The idea is to approximate a fuzzy region by a so-called plateau region consisting of a finite number of crisp regions that are all adjacent or disjoint to each other and associated with different membership values determining the degree of belonging to the fuzzy region. Geometric union, geometric intersection, and geometric difference on fuzzy regions are expressed by corresponding operations on the underlying crisp regions. We leverage that several implementations are already available for crisp regions.