Fuzzy Spatial Data Types for Spatial Uncertainty Management in Databases

Spatial database systems and geographical information systems are currently only able to support geographical applications that deal with crisp spatial objects, that is, objects whose extent, shape, and boundary are precisely determined. Examples are land parcels, school districts, and state territories. However, many new, emerging applications are interested in modeling and processing geographic data that are inherently characterized by spatial vagueness or spatial indeterminacy. This requires novel concepts due to the lack of adequate approaches and systems. In this chapter, we focus on an important kind of spatial vagueness called spatial fuzziness. Spatial fuzziness captures the property of many spatial objects in reality that do not have sharp boundaries and interiors or whose boundaries and interiors cannot be precisely determined. We will designate this kind of entities as fuzzy spatial objects. Examples are polluted areas, temperature zones, and lakes. We propose an abstract, formal, and conceptual model of so-called fuzzy spatial data types (that is, a fuzzy spatial algebra) introducing fuzzy points, fuzzy lines, and fuzzy regions in the two-dimensional Euclidean space. This chapter provides a definition of their structure and semantics, which is supposed to serve as a specification of their implementation. Furthermore, we introduce fuzzy spatial set operations like fuzzy union, fuzzy intersection, and fuzzy difference, as well as fuzzy topological predicates as they are useful in fuzzy spatial joins and fuzzy spatial selections. We also sketch implementation strategies for the whole type system and show their integration into databases. An outlook on future research challenges rounds out the chapter.