Spatial object modelling in fuzzy topological spaces with application to land cover change (2004)

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Currently most GISs represent natural phenomena by crisp spatial objects. In fact many natural phenomena have fuzzy characteristics. The representation of these objects in the crisp form greatly simplifies the processing of spatial data. However, this simplification cannot describe these natural phenomena precisely, and it will lead to loss of information in these objects. In order to describe natural phenomena more precisely, the fuzziness in these natural phenomena should be considered and represented in a GIS. This will allow the derivation of better results and a better understanding of the real world to be achieved. The central topic of this thesis focuses on the accommodation of fuzzy spatial objects in a GIS. Several issues are discussed theoretically and practically, including the definition of fuzzy spatial objects, the topological relations between them, the modeling of fuzzy spatial objects, the generation of fuzzy spatial objects and the utilization of fuzzy spatial objects for land cover changes. A formal definition of crisp spatial objects has been derived based on the highly abstract mathematics such as set theory and topology. Fuzzy set theory and fuzzy topology are the ideal tools for defining fuzzy spatial objects theoretically, since fuzzy set theory is a natural extension of classical set theory and fuzzy topology is built based on fuzzy sets. However, owing to the extension, several properties holding between crisp sets do not hold for fuzzy sets. The key issue of a fuzzy spatial object is its boundary. Three definitions of fuzzy boundary are revisited and one is selected for the definition of fuzzy spatial objects. Besides the fuzzy boundary, several notions such as the core, the internal, the fringe, the frontier, the internal fringe and the outer of a fuzzy set are defined in fuzzy topological space. The relationships between these notions and the interior, the boundary and the exterior of a fuzzy set are revealed. In general, the core is the crisp subset of the interior, and the fringe is a kind of boundary but shows a finer structure than the boundary of a fuzzy set in fuzzy topological space. These notions are all proven to be topological properties of a fuzzy topological space. The definition of a simple fuzzy region is derived based on the above topological properties. It is discussed twice in the thesis. Firstly, the definition of a simple fuzzy region is given in a special fuzzy topological space called crisp fuzzy topological space, since most topological properties of a fuzzy set in the fuzzy topological space are the same as those in crisp topological space. A formal definition of a simple fuzzy region is proposed based on the discussion of the topological properties, besides the interior, the boundary and the exterior, of a fuzzy set in the general fuzzy topological space. A crisp simple region is a special form of a simple fuzzy region. One of the fundamental properties between fuzzy spatial objects is the topological relations. This topic is intensively discussed in the thesis. The problem of the 9-intersection approach for identifying topological relations between fuzzy spatial objects is revealed. In order to derive the topological relations between fuzzy spatial objects, the 9-intersection approach is updated into the 3*3-intersection approach in the crisp fuzzy topological space. Furthermore, the 4*4-intersection matrix is built up by using the topological properties of fuzzy sets, and the 5*5-intersection matrix can be built up based on a certain condition in crisp fuzzy topological space. These matrices are then updated in the general fuzzy topological space, based on topological properties, other than the interior, the boundary and the exterior, of two fuzzy sets. Two 3*3-intersection and one 4*4-intersection matrices are introduced in the general fuzzy topological space. The topological relations between simple fuzzy regions can be identified based on the topological invariants in the intersections of the matrices. Using the empty/non-empty topological invariants in the intersections, 44 and 152 relations are derived between two simple fuzzy regions. The modeling of fuzzy spatial objects should be done not only for simple fuzzy regions, but also for fuzzy lines and fuzzy points. In order to model fuzzy lines and fuzzy points and the topological relations between fuzzy spatial objects, a fuzzy cell is proposed and a fuzzy cell complex can be constructed from fuzzy cells. A fuzzy region, a fuzzy line and a fuzzy point are then defined according to this structure. The relations between these fuzzy spatial objects are identified. The fuzzy cell complex structure constitutes a theoretic framework, since it can easily model the fuzzy spatial objects. After proposing the theoretic framework for fuzzy spatial object modeling, the thesis addresses several practical issues on applying fuzzy spatial objects. The first issue is how to generate fuzzy spatial objects. A composite method is proposed for the generation of fuzzy land cover objects. It involves several steps, from designing membership functions to classification and refining the membership values of fuzzy land cover objects. Another practical issue is how to retrieve fuzzy spatial objects, particularly on the basis of topological relations. In traditional GIS, the query operators are defined based on the relatively small number of topological relations. However, there are many topological relations between fuzzy spatial objects. In order to query fuzzy spatial objects, the query operators are proposed and formalized based on the common-sense operators in traditional GIS. The 44 or 152 topological relations are grouped into these operators by four different methods. These methods constitute a relatively complete covering for querying fuzzy spatial objects so as to meet the different application requirements. The third practical issue is how to use fuzzy spatial objects in real applications. Since the dynamics of land covers is a very important topic in China, the focus lies on calculating changes of land covers. Sanya city, located in south China, is selected as the test area. A fuzzy reasoning method is proposed for calculating land cover changes. It shows that, with fuzzy representation, not only can a better result be achieved for the land cover changes, but also the details of changes can be revealed.
Year: 2004
ISBN: 90-6164-220-5
Language: English
Page: 219
Thesis note: Thesis (Ph. D.) - University of Twente, Wageningen, The Netherlands

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