Over the years database management systems have evolved to include spatially referenced data. Because spatial data are complex and have a number of unique constraints~i.e., spatial components and uncertain properties!, spatial database systems can be effective only if the spatial data are properly handled at the physical level. Therefore, it is important to develop an effective spatial and aspatial indexing technique to facilitate flexible spatial and/or aspatial querying for such databases. For this purpose we introduce an indexing approach to use~fuzzy! spatial and fuzzy! aspatial data. We use a number of spatial index structures, such as Multilevel Grid Filẽ MLGF!, G-tree, R-tree, and R * -tree, for fuzzy spatial databases and compare the performances of these structures for various flexible queries.
Abstmcl-Database systems can be effective only if the data are properly handled at the physical level. Therefore, it is important to develop an effective spatial and aspatial indexing technique to facilitate flexible spatial andlor asprtial querying for spatial databases. In this study we adapt a number of spatial index structures, such as Multilevel grid file (MLGF), G-tree, R-tree, and R*-tree, for fuzzy spatial databases and compare the performances of these structures for various flexible queries. r. INTRODUCTIONThe effectiveness of spatial database systems can be severely compromised if the spatial data are not properly managed at the physical level. Spatial databases are characterized by large quantities of data. Since spatial data are usually complex and have a number of unique requirements (such as spatial components and uncertainty), classical one-dimensional database indexing structures are not appropriate for multi-dimensional spatial searching. Therefore, there exist some dedicated spatial access structures for indexing spatial attributes. These structures use multi-dimensional access methods [4]. which comprise: a transformation approach, overlapping regions, clipping, and multi layers. Among the existing spatial index structures, the R-tree [SI and R*-tree [2] were proposed by the overlapping regions method. The R+-tree [ 1 I] uses the clipping method; Z-ordering and Hilbert curve [I$] are the most prominent methods in the transformation methods, and Multi-level Grid File (MISF) [14] and G-tree [SI are examples of the Multi Layers approach. The other approach for developing spatial access structures is to adapt a conventional indexing method for spatial indexing. For example, kD-trees and its variations have been derived from binay trees. The other adapted example index structures are the LSD-tree [7]. EXCELL, [13], the buddy hash tree [12], the BANG File [3]. and the hB-tree [9].An additional, inevitable property of spatial data is the need to represent uncertainty, since information in many spatial database applications may be not only complex but also uncertain. Uncertainty might arise from data/objects and/or relationships between the spatial objects. More specilically, the need to incorporate uncertainty in spatial database applications arises from the following reasons:( 1) some geographic information in GIS applications is inherently imprecise or fuzzy. For example, locations of geographic objects, some spatial relationships and various geometric and topological properties usually involve various forms of uncertainty.(2) In addition, most natural geographic phenomena have uncertain boundaries: For example. mountains, lakes. soils, and slope.(3) Some measurements related to the spatial domain are often imprecise. Sometimes forcing such data to be completely crisp may result in false and useless information. (4) In spatial database applications, some of the spatial domain related knowledge is specified in natural languages by using fuzzy terms and numerous quantifiers (e.g. many, few, some, alm...
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