Spatial Plateau Algebra: An Executable Type System for Fuzzy Spatial Data Types

Many geographical applications have to deal with spatial objects that reveal an intrinsically vague or fuzzy nature. A spatial object is fuzzy if locations exist that cannot be assigned completely to the object or to its complement. Spatial database systems and Geographical Information Systems are currently unable to cope with this kind of data. Based on an available abstract data model of fuzzy spatial data types for fuzzy points, fuzzy lines, and fuzzy regions, this paper proposes the Spatial Plateau Algebra that provides spatial plateau data types as an executable type system for fuzzy spatial data types. Each spatial plateau object consists of a finite number of crisp counterparts that are all adjacent or disjoint to each other, are associated with different membership values, and hence form different plateaus. The formal framework and the implementation are based on well known, exact models and available implementations of crisp spatial data types. Spatial plateau set and metric operations as well as spatial plateau topological predicates on spatial plateau objects are expressed as a combination of geometric methods on the underlying crisp spatial objects. This paper offers a conceptually clean specification for implementing a database extension for fuzzy spatial objects and their operations and predicates. Further, we demonstrate the embedding of these new data types as attribute data types in a database schema as well as the incorporation of fuzzy spatial operations and predicates into a database query language.