Soft Computing Techniques in Spatial Databases

Soft Computing Techniques in Spatial Databases

Markus Schneider (University of Florida, USA)
DOI: 10.4018/978-1-60566-814-7.ch004
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Abstract

Spatial database systems and geographical information systems are currently only able to support geographical applications that deal with only 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. Examples are air polluted areas, temperature zones, and lakes. These applications require novel concepts due to the lack of adequate approaches and systems. In this chapter, the authors show how soft computing techniques can provide a solution to this problem. They give an overview of two type systems or algebras that can be integrated into database systems and utilized for the modeling and handling of spatial vagueness. The first type system, called Vague Spatial Algebra (VASA), is based on well known, general, and exact models of crisp spatial data types and introduces vague points, vague lines, and vague regions. This enables an exact definition of the vague spatial data model since we can build it upon an already existing theory of spatial data types. The second type system, called Fuzzy Spatial Algebra (FUSA), leverages fuzzy set theory and fuzzy topology and introduces novel fuzzy spatial data types for fuzzy points, fuzzy lines, and fuzzy regions. This enables an even more fine-grained modeling of spatial objects that do not have sharp boundaries and interiors or whose boundaries and interiors cannot be precisely determined. This chapter provides a formal definition of the structure and semantics of both type systems. Further, the authors introduce spatial set operations for both algebras and obtain vague and fuzzy versions of geometric intersection, union, and difference. Finally, they describe how these data types can be embedded into extensible databases and show some example queries.
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Introduction

Spatial database systems (SDBS) are full-fledged database systems which, in addition to the functionality of standard database systems for alphanumeric data, provide special support for the storage, retrieval, management, and querying of spatial data, that is, objects in space. In particular, SDBS are used as the data management foundation of Geographic Information Systems (GIS). In the literature, the common consensus prevails that special data types are necessary to adequately model geometry and to efficiently represent geometric data in database systems. These data types are commonly denoted as spatial data types (Schneider 1997) such as point, line, and region. We speak of spatial objects as instances of these data types. So far, the mapping of spatial phenomena of the real world leads almost exclusively to precisely defined spatial objects. Spatial data modeling implicitly assumes that the positions of points, the locations and routes of lines, and the extent and hence the boundary of regions are precisely determined and universally recognized. This leads to exact object models. Examples are especially man-made spatial objects representing engineered artifacts (like monuments, highways, buildings, bridges) and predominantly immaterial spatial objects exerting social control (like countries, districts, and land parcels with their political, administrative, and cadastral boundaries). We denote this kind of entities as crisp or determinate spatial objects.

But for many geometric applications, the mapping into crisp spatial objects is an insufficient abstraction process since many geographic objects show the inherent feature of spatial vagueness or spatial indeterminacy (Burrough & Frank 1996). Current GIS and spatial database systems are not capable of supporting applications based on vague geometric data. In these applications, the positions of points are not exactly known, the locations and routes of lines are unclear, and regions do not have sharp boundaries, or their boundaries cannot be precisely determined. Examples are natural phenomena (like soil quality, vegetation, oceans, valleys, mountains, oil fields, biotopes, deserts, clouds, temperature zones, air pressure, sandbanks), cultural phenomena (like a Rhaeto-Romanic language speaking area) and social phenomena (like population density, unemployment rate, air pollution emission, terrorists’ refuges and escape routes). We denote this kind of entities as vague or indeterminate spatial objects.

This chapter shows that and how different soft computing techniques can be leveraged to represent spatial vagueness. It gives an overview of two different type systems that can be integrated into database systems and whose types can be employed as attribute types in the same way as standard data types like integer or string. A fundamental design concept is that these new types are not represented through a database model (for example, relational, object-oriented, complex data model) but through abstract data types that encapsulate and hide the internal complexity of their values. This implies that a database model and its underlying theoretical framework (for example, relational database theory) does not have to be modified in any manner. The first type system, called Vague Spatial Algebra (VASA), is based on well known, general, and exact models of crisp spatial data types and introduces vague points, vague lines, and vague regions. This enables an exact definition of the vague spatial data model since we can build it upon an already existing theory of spatial data types. The second type system, called Fuzzy Spatial Algebra (FUSA), leverages fuzzy set theory and fuzzy topology and introduces novel fuzzy spatial data types for fuzzy points, fuzzy lines, and fuzzy regions. This enables an even more fine-grained modeling of spatial objects that do not have sharp boundaries and interiors or whose boundaries and interiors cannot be precisely determined.

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