| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 495706 | Applied Soft Computing | 2014 | 23 Pages |
•We provide an implementation concept called Spatial Plateau Algebra for fuzzy points, fuzzy lines, and fuzzy regions.•Spatial plateau objects are described by collections of crisp spatial objects like crisp points, lines, and regions.•Spatial plateau operations are expressed as combinations of crisp spatial operations and are thus directly executable.•The new data types can be embedded as attribute data types in a database schema.•The operations can be incorporated into queries formulated in an extension of SQL, the standard database query language.
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 (GIS) 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 that leverages fuzzy set theory and fuzzy point set topology, this article proposes a Spatial Plateau Algebra that provides spatial plateau data types as an implementation of 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 implementations of crisp spatial data types. Spatial plateau operations as geometric operations on spatial plateau objects are expressed as a combination of geometric operations on the underlying crisp spatial objects. This article offers a conceptually clean foundation for implementing a database extension for fuzzy spatial objects and their operations, and demonstrates the embedding of these new data types as attribute data types in a database schema as well as the incorporation of fuzzy spatial operations into a database query language.
