This paper explains why and how spatial databases and geographic information systems can beneﬁt from an appropriate representation of imprecise and/or uncertain information. Not only are the imprecission and uncertainty inherent to the data to be modeled, they also appear in both various queries and the result of various queries

De Caluwe, Rita

Verstraete, Jörg

English

Ghent University Academic Bibliography

Fuzziness in Spatial Databases and GISJo¨rg Verstraete, Rita De CaluweAbstract— This paper explains why and how spatialdatabases and geographic information systems can benefitfrom an appropriate representation of imprecise and/or un-certain information. Not only are the imprecission and un-certainty inherent to the data to be modeled, they also ap-pear in both various queries and the result of various queries.Keywords— spatial database, GIS, fuzzy, uncertainty, im-precision, fuzzinessI. IntroductionFUZZY SET THEORY (introduced in 1965 by L.A.Zadeh [1]) and the related fuzzy logic are extensionsof the traditional set theory and binary logic. They haveprovided new, more suitable means to model imprecissionand uncertainty. The data to be dealt with in real life,commonly are only known approximately and many propo-sitions are not strictly true or false.Up to now, these theories have been used successfully forthe modeling of numerous applications, ranging from data-analysis and planning, to decision support systems andprocess control. Applications of fuzzy logic are probablybest known in the latter field. Of course, during the pastdecades, the theories have been further developed and re-fined [2]and their applications have become more and morewidespread [3].A new emerging and challenging application, can befound in the field of Geographic Information Systems(GIS), at the heart of which are spatial databases. Dueto the nature of the geographic information, there are par-ticular problems and limitations, which are the subject ofthis PhD-research.II. Traditional Spatial Databases and GISA. Data: Features, Objects and LayersIt is a misconception that a geographic information sys-tem merely contains maps [4]. In a GIS, features and in-formation about these features are stored. A feature canrange from names, locations, dates to numerical data (mea-surements, statistics, . . . ) and maps. The notion featurecorresponds to what in the spatial database is called anobject (note that is does not imply that a spatial databasehas to be an object-oriented database). An object mayhave four types of attributes: spatial (where an object is),temporal (when an object is), thematic (what an object is)and scale (how an object is).It must be possible to store the data in a spatialdatabase, as well as perform operations on the objectsJ. Verstraete and R. De Caluwe are with the Department ofTelecommunications and Information Processing, Ghent University(RUG), Gent, Belgium. E-mail: {jorg.verstraete, rita.decaluwe}@telin.rug.ac.be .(or attributes) of data, hence spatial queries must be sup-ported, which will be addressed in the next section.Traditionally, features are stored in layers. A layer is agroup of features, or a usable subset of a dataset, generallycontaining objects of certain classes (e.g. layers containingroads, layers containing mountains, . . . ). In order to solvea query, data of several layers are often needed. Multiplelayers can be combined: they are superimposed in such away that the resultant set would contain the features ofthe different layers. Superimposition of the required layersis called an overlay, and is a technique, additional to thedifference and intersection operations, used to solve queries.B. QueriesThe main purpose of a GIS is the querying and analy-sis of the contained data. An example of a simple query(which involves a single layer) is “What is the name of themountain at a given particular point on the map?” To ob-tain the result, it would suffice to look up the longitude andlatitude for the selected point, and determine the name ofthe mountain by looking at the mountain layer.A more complex query (involving several layers, thus re-quiring the overlay-technique) is “Display all skiable moun-tains within ten kilometers of an airport”. This query ob-viously requires several operations on the spatial data. Tostart the overlay-process, we could look at the mountainlayer, and eliminate all non-skiable mountains (which couldbe contained in a different layer). The next step would thenbe to overlay this with a layer containing all the airports,and to draw circles with a ten kilometer radius around eachairport. The answer of the query, contained in the resul-tant layer, can then be returned to the user. In general, aGIS should be able to support the handling of five differenttypes of queries [4]:• Location queries: What is at a given position? Insteadof this position being given by coordinates (latitude andlongitude), it could also be indicated by the name of amountain, a zipcode, the name of a building, or a set ofconstraints that pinpoint a location.• Condition queries: What locations satisfy a given set ofconditions? A set of conditions is listed, and GIS is ex-pected to return every point that satisfies these conditions(e.g. one could query a GIS for the names of mountainswhich exceed a given altitude and are located in Europe.)• Trends: What has changed since a given point in time ?Only GIS that consider the notion of time can handle thistype of query, unfortunately not all GIS allow the temporalaspect to be taken into consideration. In the case of anyGIS however, the incorporation of the notion of time wouldbe very interesting. For example, when considering the soildata set of a mountain range, having several successive setsof the same geographic area would let us determine the rateof erosion.• Patterns: What spatial patterns exist? This more com-plex and sophisticated kind of query could for example beused to find the origin of a certain pollutant, given infor-mation about how this type of pollutant disperses.• Simulation: These types of query are useful for planningand prediction about future evolutions. They allow theuser to pose questions regarding “What happens if . . . ”.III. Fuzziness in Spatial Databases and GISImprecission and uncertainty can appear both in thedata to be modeled in the GIS as in the query itself. Thetraditional modeling of these semantic notions is howeververy basic (few or no information about the accuracy of cer-tain values is considered). The occurrence of imprecissioncan be illustrated by reconsidering the previous example“Display all skiable mountains within ten kilometers of anairport”.The first issue is the meaning of the term “within tenkilometers”. While this could be a useful stipulation, it ispossible that is not intended in a clear cut way. Locationson a distance of 10.1 km might still be acceptable, 10.2km might be less acceptable, but e.g. 11 km might beunacceptable. Besides, should ten kilometers be consideredin a straight line, or along real, existing roads ? It mightalso be desirable for the GIS to be queried using linguisticterms such as walking distance, in order to provide a morenatural way of querying.The next issue is the term airport. Do we consider asmall airfield, only meant for private, recreational flightsor should only the large commercial airports be taken intoaccount, or are both alternatives valid ? 1The term skiable depends heavily on the capacities ofthe person posing the question. Some slopes might be con-sidered skiable for an experienced athlete, but at the sametime not at all skiable for the occasional tourist. While thisterm could be interpreted by having the user specify whathe/she considers skiable, this is not straightforward.An example of uncertainty is e.g. when somebody re-members a hotel in a ski-resort, but is uncertain about thecity in which it is located. It could be in city A or B.These examples illustrate that – although it is unlikelythat every problem will be solved – an appropriate repre-sentation of the imprecission and uncertainty would allowfor a more realistic modeling of numerous data.IV. Research ObjectivesThe purpose of this PhD-work is to define a formal modelto work with imprecise and uncertain spatial data, and todevelop and evaluate techniques to store and manipulatesuch data in a prototype implementation.Fuzzy set theory will be used to model the imprecissionand uncertainty concerning the information. Every elementof a fuzzy set has associated with it a number (in the range0 to 1) which represents the degree to which it belongs tothe set. This number is the membership degree. As fuzzy1In the English language, there is a difference between airport, air-field and airstrip, but the example is only meant as an illustration.set theory is an extension of the traditional set theory, crispdata can also be modeled using this theory. The operatorsof the traditional set theory have been generalized to beapplicable on fuzzy sets, yet the definition of some specificspatial operators will also need to be generalized in orderfor them to be applicable on fuzzy sets.Fuzzy propositional logic – which is an extension of thetraditional propositional logic – will provide the basis forthe definition of appropriate fuzzy querying methods.Conceptually, several methods for representing fuzzyspatial data are possible. A first intuitive representationis by means of contourlines [5,6], simply put : a set of linesconnecting points ,which have the same membershipdegreefor a specific feature, are used to represent the data. Whilethis is a good representation from a human point of view,it is not that interesting a representation to work with dueto its increasing complexity when operations have to be ap-plied on them. Currently, a representation based on a tri-angulated irregular network (TIN for short) is being inves-tigated. A TIN is a network of triangles, the vertex pointsof which are all datapoints (these are points for which thereis knowledge about a certain feature, the information aboutpoints in between will be obtained through interpolation).A grid of triangles form a TIN if the following property issatisfied: three vertex points define a triangle if and only ifthe circle defined by them contains no other vertex points.Except for degenerate cases (four points that are locatedat the corners of the same square, . . . ), a unique TIN canbe constructed. Additionally, there are rules that uniquelydefine the TIN in these degenerate cases. Commonly themethod of Delaunay-triangulation is used to construct tri-angulated irregular networks. These triangulated irregularnetworks have a relatively simple structure, yet are veryflexible to use.In order to implement these representations for a realapplication, appropriate data structures need to be defined.These data structures can not only be used to representfuzzy data in the spatial database itself, but could also beuseful to store intermediate data (needed while processinga query) or to store the result of the query (even if thisresult does not need to be persistent).At a first stage, all these problems are approached in aformal way, but we will also thrive to provide prototype-implementations suitable to test the developed techniques.These will most likely be the implementations of severalstand-alone sub-problems than a full GIS-implementation.References[1] Lotfi Zadeh “Fuzzy Sets”, Information and Control, textbf1 3(1965) 338-353.[2] Didier Dubois, Henri Prade “ Fundamentals of Fuzzy Sets”Kluwer Academic Publishers, 2000.[3] Hans-Ju¨rgen Zimmerman Practical Applications of Fuzzy Tech-nologies, Kluwer Academic Publishers, 1999.[4] Ashley Morris, Why Spatial Databases Need Fuzziness, proc. ofNafips 2001, pp. 2446-2451.[5] Eliseo Clementini, Paoline Di Felice, An algebraic model for spa-tial objects with undetermined boundaries, GISDATA SpecialistMeeting - revised version, 1994.[6] Nicholas Mark Gotts, Anthony G. Cohn, A mereological approachto representing spatial vagueness, Working Papers, Ninth Inter-national Workshop on Qualitative Reasoning, 1995, pp. 246-255.

Fuzziness in spatial databases and GIS

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Fuzziness in spatial databases and GIS

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