Field Based Methods for the Modeling of Fuzzy Spatial Data

Verstraete, Jörg; Tré, Guy De; Caluwe, Rita De; Hallez, Axel

doi:10.1007/3-540-26886-3_3

Cited by 24 publications

(11 citation statements)

References 11 publications

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“…An interesting alternative is the approach in [48] which provides two models for fuzzy spatial data. The first one is a raster (bitmap) approach, and the second one is a vector-based approach based on triangulated irregular networks (TINs).…”

Section: Approaches To Implementing Fuzzy Spatial Objectsmentioning

confidence: 99%

“…To be able to produce correct result values, algorithms need correct input values; otherwise, algorithms will fail and produce invalid results. Beside the Vague Spatial Algebra with its restricted logic, only the TIN-based model in [48] fulfills closure properties. Although the intersection, union, and difference of two TINs is usually not a TIN, a Delaunay triangulation can help us transform the intermediate intersection result into a TIN.…”

Section: Approaches To Implementing Fuzzy Spatial Objectsmentioning

confidence: 99%

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Spatial Plateau Algebra for implementing fuzzy spatial objects in databases and GIS: Spatial plateau data types and operations

Schneider

2014

Applied Soft Computing

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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.

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Section: Approaches To Implementing Fuzzy Spatial Objectsmentioning

confidence: 99%

Section: Approaches To Implementing Fuzzy Spatial Objectsmentioning

confidence: 99%

Spatial Plateau Algebra for implementing fuzzy spatial objects in databases and GIS: Spatial plateau data types and operations

Schneider

2014

Applied Soft Computing

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“…This set can the be augmented to a fuzzy set, thus allowing each point to have a membership grade. An overview of this model was presented in [5]. Fig.…”

Section: Fuzzy Regionsmentioning

confidence: 99%

“…To consider the complexity of the operators, first more practical models should be derived. This is currently in progress, and we are working on similar approaches as for the simple fuzzy regions: these were approximated using triangular networks or bitmaps ( [5], [11], [12]). The same representation can be used for the candidate fuzzy regions, in which case the complexity depends on both the representation methods uses and the number of candidate regions involved.…”

Section: Construction Of and Reasoning With Level-2 Regionsmentioning

confidence: 99%

Higher Reasoning with Level-2 Fuzzy Regions

Verstraete

2011

Flexible Query Answering Systems

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Abstract. Spatial data is quite often is prone to uncertainty and imprecision. For this purpose, fuzzy regions have been developed: they basically consist of a fuzzy set over a two dimensional domain, allowing for both fuzzy regions and fuzzy points to be modelled. The model is extended to a level-2 fuzzy region to overcome some limitations, but this has an impact on operations. In this contribution, we will look into the construction of and combination of existing data to yield level-2 fuzzy regions.

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“…Type-2 fuzzy sets are mentioned by Verstraete et al (2005) as being possible within their method, although they do not go into any detail, while Du and Zhu (2006) give a theoretical treatment for type-2 spatial fuzzy sets. On the other hand, previous research by Fisher et al (in press) has directly explored methods for populating type-2 fuzzy sets for spatial information.…”

Section: Introductionmentioning

confidence: 99%

Higher Order Vagueness in a Dynamic Landscape: Multi-Resolution Morphometric Analysis of a Coastal Dunefield

Fisher

Wood²,

Cheng³

2007

J ENV INFORM

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ABSTRACT. Many environmental phenomena can be conceptualised as vague and so may be suitable for storage as fuzzy sets and analysis by fuzzy logic. Fuzzy sets directly address the vagueness in the information, but many consider that any statement about a vague phenomenon must itself be vague. This is known as higher order vagueness, and is handled in fuzzy set theory by type-2 and, by extension, type-n fuzzy sets. In this paper we use the recognition of, and change in, a system of coastal sand dunes as an environmental example in which to explore the use of type-2 fuzzy sets. The crests and troughs of the dunes are identified as fuzzy sets from geomorphometric analysis of high resolution digital elevation models from two years (1998 and 2000). By varying the parameters of the morphometric extraction, multiple instances of type-1 fuzzy sets can be defined, and these can be summarised to yield type-2 fuzzy sets. The logic of change analysis is presented, and two alternative approaches to change analysis of type-2 fuzzy sets implemented. In one approach changes in the multiple instances of type-1 fuzzy sets are analysed and summarised as type-2 sets. The second approach directly examines change in the parameters of type-2 fuzzy sets, viewing the results for the different parameters as separate instances of change. All analyses produce satisfactory results which, although they are hard to verify, make sense, yielding a range of possible but small degrees of fuzzy change. In a rather sedentary dune system (as is usual in a coastal location in mid-latitudes) this is to be expected. Change analysis in most applications of type-2 fuzzy sets, which might be based on expert advice for defining memberships, would have to rely on this second approach, and it is therefore interesting to note that this yields the largest range of possible change results.

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Field Based Methods for the Modeling of Fuzzy Spatial Data

Cited by 24 publications

References 11 publications

Spatial Plateau Algebra for implementing fuzzy spatial objects in databases and GIS: Spatial plateau data types and operations

Spatial Plateau Algebra for implementing fuzzy spatial objects in databases and GIS: Spatial plateau data types and operations

Higher Reasoning with Level-2 Fuzzy Regions

Higher Order Vagueness in a Dynamic Landscape: Multi-Resolution Morphometric Analysis of a Coastal Dunefield

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