Schneider, M. 1999, Uncertainty Management for Spatial Data in Database: Fuzzy Spatial Data Types. The 6th Int. Symp. on Advances in Spatial Databases(SSD), LNCS 1651, Springer Verlag, 330-351.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....area which definitely belongs to the vague region. The boundary region describes the area for which it is not sure whether it or parts of it belong to the vague region or not. Models based on rough sets [16] work with lower and upper approximations of spatial objects. Models based on fuzzy sets [1, 13, 14] model the vagueness resulting from the imprecision of the meaning of a concept. A concept like ocean or Southern England cannot be modeled with crisp but with fuzzy means. Fuzzy spatial data types defined on an abstract (Euclidean space) and on a discrete (grid partition) geometric basis are ....

....resulting from the imprecision of the meaning of a concept. A concept like ocean or Southern England cannot be modeled with crisp but with fuzzy means. Fuzzy spatial data types defined on an abstract (Euclidean space) and on a discrete (grid partition) geometric basis are introduced in [13, 14]. 2.2 Crisp and Fuzzy Topological Predicates Our definitions are based on the so called 9 intersection model [6] from which a complete collection of mutually exclusive topological relationships can be derived for each combination of spatial types. The model is based on the nine possible ....

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M. Schneider. Uncertainty Management for Spatial Data in Databases: Fuzzy Spatial Data Types. 6th Int. Symp. on Advances in Spatial Databases, LNCS 1651, pp. 330--351. Springer-Verlag, 1999.

....14] have been proposed, but these are not suitable for an integration into a database system, because they do not provide data types for fuzzy spatial data. The author himself has started to work on this topic and to design a system of fuzzy spatial data types including operations and predicates [10, 11] that can be embedded into a DBMS. The goal of this paper is to give a definition of topological predicates on fuzzy regions, which is currently an open problem, and to discuss some properties of these predicates. Besides, we show the integration of these predicates into a query language. Section ....

....of topological predicates for fuzzy regions on these topological predicates for complex crisp regions. 3. MODELING FUZZY REGIONS A structureless definition of fuzzy regions in the sense that only flat point sets are considered and no structural information is revealed has been given in [10]. For our purposes we deploy a semantically richer characterization and approximation of fuzzy regions and define them in terms of special, nested a cuts. A fuzzy region F is described as a collection of crisp a level regions 1 [10] i.e. F = fF a 1 ; F a n 1 g where a i 2 L F , ....

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M. Schneider. Uncertainty Management for Spatial Data in Databases: Fuzzy Spatial Data Types. 6th Int. Symp. on Advances in Spatial Databases, LNCS 1651, pp. 330--351. Springer-Verlag, 1999.

....on fuzzy spatial objects. Examples are the area operation on fuzzy regions or the length operation on fuzzy lines. It turns out that their definition is not as trivial as the definition of their crisp counterparts. The underlying formal object model follows the author s previous work in [8] and offers fuzzy spatial data types like fuzzy regions and fuzzy lines in two dimensional Euclidean space. Our concept to integrate fuzzy spatial data types into databases is to design them as abstract data types whose values can be embedded as complex entities into databases [9] and whose ....

....of an object which certainly has an extent but which inherently cannot or does not have a precisely definable boundary (e.g. between a mountain and a valley) This kind of vagueness results from the imprecision of the meaning of a concept. Models based on fuzzy sets have, e.g. been proposed in [1, 2, 4, 8]. 3. FUZZY SPATIAL OBJECTS In this section we very briefly and informally present the basic elements of an abstract model for fuzzy spatial objects as it has been formalized in [8] The model is based on fuzzy set theory (and fuzzy topology) whose main concepts are introduced first, as far as ....

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M. Schneider. Uncertainty Management for Spatial Data in Databases: Fuzzy Spatial Data Types. In 6th Int. Symp. on Advances in Spatial Databases, LNCS 1651, pages 330--351. Springer-Verlag, 1999.

.... and upper approximations of spatial objects, 3) probabilistic models (for example, Burrough, 1996; Shibasaki, World Scientific, 1993) which predominantly model positional and measurement uncertainty, and (4) models based on fuzzy sets (for example, Altman, 1994; Burrough, 1996; Dutta, 1989; Schneider, 1999) which predominantly model fuzziness. The vagueness represented by fuzziness, in which we are only interested in this paper, does not describe the uncertainty of expectation like in probabilistic models but the vagueness resulting from the imprecision of the meaning of a concept. Examples of fuzzy ....

....grey values in images which are used to visualize different levels of intensity of an attribute. 4.2 Formal Definition of Fuzzy Regions The aim of this section is to develop and formalize our concept of discrete crisp and fuzzy regions. A detailed classification of fuzzy regions can be found in (Schneider, 1999). Our main interest concerns a structured view of discrete fuzzy regions. We start with the definition of a fuzzy grid unit. For this purpose we have to appropriately assign labels to its 2 cell, its four 1 cells, and its four 0 cells. The membership value of a grid unit as a whole is dominated ....

[Article contains additional citation context not shown here]

Schneider, M. (1999). Uncertainty Management for Spatial Data in Databases: Fuzzy Spatial Data Types. 6th Int. Symp. on Advances in Spatial Databases. LNCS 1651. Springer-Verlag, 330--351.

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Schneider, M. 1999, Uncertainty Management for Spatial Data in Database: Fuzzy Spatial Data Types. The 6th Int. Symp. on Advances in Spatial Databases(SSD), LNCS 1651, Springer Verlag, 330-351.

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Schneider, M.: Uncertainty management for spatial data in databases: Fuzzy spatial data types. Lecture Notes in Computer Science 1651 (1999) 330--351

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M. Schneider. Uncertainty Management for Spatial Data in Databases: Fuzzy Spatial Data Types. SSD 1999: 330-351.

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