Fuzzy Modeling with Spatial Information for Geographic Problems

342 Pages·2005·8.226 MB·english

by  Frederick E. Petry, Vincent B. Robinson, Maria A. Cobb (eds.)

Frederick E. Petry
Vincent B. Robinson
Maria A. Cobb
(Editors)
Fuzzy Modeling with
Spatial Information for
Geographic Problems
With 135 Figures
123
Professor Dr. Frederick E. Petry
Tulane University, Dept.of Electrical Engineering and Computer Science
310 Stanley Thomas Hall, New Orleans LA 70118
USA
e-mail: [e-mail]
Professor Dr. Vincent B. Robinson
University of Toronto at Mississauga, Dept. of Geography
3359 Mississauga Road North, Mississauga, Ontario
Canada L5L 1C6
e-mail: [e-mail]
Professor Dr. Maria A. Cobb
University of Southern Mississippi, Dept. of Computer Science and Statistics
Hattiesburg MS 39406-5106
USA
e-mail: [e-mail]
Library of Congress Control Number: 2004115949
ISBN 3-540-23713-5 Springer Berlin Heidelberg New York
© Springer-Verlag Berlin Heidelberg 2005
Printed in Germany
Foreword
The capabilities of modern technology are rapidly increasing, spurred on to a
large extent by the tremendous advances in communications and computing.
Automated vehicles and global wireless connections are some examples of these
advances. In order to take advantage of such enhanced capabilities, our need to model
and manipulate our knowledge of the geophysical world, using compatible
representations, is also rapidly increasing. In response to this one fundamental issue
of great concern in modern geographical research is how to most effectively capture
the physical world around us in systems like geographical information systems (GIS).
Making this task even more challenging is the fact that uncertainty plays a pervasive
role in the representation, analysis and use of geospatial information. The types of
uncertainty that appear in geospatial information systems are not the just simple
randomness of observation, as in weather data, but are manifested in many other forms
including imprecision, incompleteness and granularization. Describing the uncertainty
of the boundaries of deserts and mountains clearly require different tools than those
provided by probability theory. The multiplicity of modalities of uncertainty appearing
in GIS requires a variety of formalisms to model these uncertainties. In light of this it
is natural that fuzzy set theory has become a topic of intensive interest in many areas
of geographical research and applications
This volume, Fuzzy Modeling with Spatial Information for Geographic Problems,
provides many stimulating examples of advances in geographical research based on
approaches using fuzzy sets and related technologies. It includes chapters on diverse
research topics such as spatial directions, geographical interpolation, landscape
features and spatial decision systems among others. The editors, Maria Cobb, Vince
Robinson and Fred Petry provide a snapshot of current topics of research and should
stimulate work in this area and hopefully encourage more cross-disciplinary efforts
such as demonstrated by these chapters. The papers published in this volume should
be of considerable interest to a broad spectrum of researchers in the fuzzy set and GIS
areas as well as those engineers who make use of geospatial information in their
applications and systems.
Ronald R. Yager
New York, NY USA
August 25, 2004
Preface
This volume, the companion to Flexible Querying and Reasoning in Spatio-
Temporal Databases edited by Rita De Caluwe, Guy De Tre, and Gloria Bordogna,
focuses on advances in research on approaches to incorporating explicit handling of
uncertainty, especially by fuzzy sets, to address geographic problems. Over the past
several years interest in the use of fuzzy approaches has grown across a broad
spectrum of fields that use spatial information to address geographic problems.
The reasoning about geographic information representing regions, relations,
and/or fields is fundamental to any progress in the application of fuzzy sets to
modeling geographical problems. There are several papers in this volume that advance
our understanding of these fundamental issues. Hans Guesgen builds on his previous
work that introduces fuzzy sets into the artificial intelligence community’s RCC
theory. His results suggest that the formalism developed by converting RCC8 relations
into fuzzy sets and applying a fuzzy RCC8 algorithm is robust under uncertainty.
Pascal Matsakis and Dennis Nikitenko focus on issues of modeling fuzzy spatial
relations. They introduce the Force Histogram (F-histogram) and proceed to illustrate
that the F-histogram is a valuable tool for extracting directional and topological
relationship information from two spatial objects exploiting a fuzzification of Allen
relations.
Much of the research on fuzzy modeling applied to geographical problems is
based on a geographic information system that represents information as layers and
uses a field based approach to processing the spatially explicit data. Jörg Verstraete
and colleagues present their exploration of two types of field based methods for the
modeling of fuzzy spatial data. They discuss the extended triangulated irregular
networks and extended bitmap models with respect to fuzzy membership values, fuzzy
numbers, operations, type-2 fuzzy sets, and possibilistic truth values. Thus, it is an in
depth exploration of fuzzy extensions to two very important, fundamental models of
geographic information.
Sungsoon Hwang and Jean-Claude Thill model localities as fuzzy regions
represented as eggs in the egg-yolk model of spatial representation. Their study
illustrates a real world problem domain where fuzzy regions and linguistic variables
are shown to be useful in addressing the problem of pinpointing the location of a
traffic accident given limited and imprecise (e.g. linguistic) information. In the case of
emergency dispatch operations, the outcome of this process could have profound
consequences.
One of the most common approaches to fuzzy modeling of spatial data for
geographical problem solving consists of constructing a fuzzy classification. The
fuzzy k-means algorithm has a long history of being applied to geographical problems.
Zhijan Liu and Roy George propose an extension to the fuzzy k-means algorithm to
account for both spatial and temporal data. They demonstrate its utility in another
important problem area of geographical data analysis, namely data mining, by
showing that it is able to identify interesting phenomena with a large weather data set.
Cidália Fonte and Weldon Lodwick identify four different sources of fuzziness in their
two phase classification procedure. For each source of fuzziness, a method to compute
the membership grades for fuzzy geographical entities is presented, based on semantic
interpretation of the grades of membership. These semantic interpretations are the
likelihood view, the random set view and the similarity view. They show that these
semantic interpretations are suitable for construction of fuzzy geographical entities.
Although spatial interpolation is a commonly used technique in geographical
analysis, the use of fuzzy spatial interpolation is not yet widespread, especially when
incorporating temporal dynamics. Suzana Dragi(cid:252)evi(cid:252) presents the potential of using
fuzzy set theory to deal with imperfect geographic data and entities when applying
GIS based spatial and spatio-temporal interpolation.
Susan Kratochwill and Josef Benedikt present the argument that the uncertainty
inherent in geographic information systems is due to the semantics of categorization
using linguistic symbols in a process of communication. They go on to present the
Talking Space platform for mapping spatial knowledge with uncertainty. Ferdinando
Di Martino and colleagues show how the FUZZY-SRA software tool is used to
evaluate the reliability of environmental data for the island of Procida.
Landscape features have long been recognized as being inherently fuzzy
concepts whose inherent fuzziness has historically been difficult to represent in a
manner that is flexible enough to be useful in any but a single problem domain
operating at a single scale. Xun Shi and colleagues present a similarity-based method
for deriving fuzzy representation of terrain features such as ridges (broad vs narrow),
headwaters, and “knobs” that is computationally efficient, effective and flexible. Peter
Fisher and colleagues explain the effect that scale has on how landscape features can
be modeled using fuzzy sets. This paper represents one of the first to explicitly model
landscape morphometry at multiple scales using fuzzy sets.
With the rapid escalation in computational technology and digital geographic
data fuzzy modeling of spatial data has become increasingly important in those
applications where decision making is of utmost importance. Frank Witlox and Ben
Derudder elaborate on fuzzy decision tables as an important addition to qualitative
modeling. They show it is possible to explicate the imprecision involved in the
decision making process through use of fuzzy decision tables and discuss possible
limitations, especially in relation to the use of fuzzy knowledge based systems. Ashley
Morris and Piotr Jankowski present the FOOSBALL system that allows for multiple
criteria fuzzy queries over an object oriented spatial database. Vince Robinson and
Phil Graniero present a computational framework and methodology for modeling
small mammals as mobile fuzzy agents making decisions during their dispersal
process.
This book has the two aims. One is to stimulate further research in both the
theory and application of fuzzy sets to spatial information management and geographic
problem solving. The other is to show the advances in research that have matured to
the point that we find fuzzy modeling being used by geoscientists, computer scientists,
geographers, ecologists, engineers, and others.
Acknowledgements
We would like to thank the authors of the papers. Reviewing and editing their
interesting contributions was a pleasure. We would especially like to thank the
anonymous referees who so generously gave of their time and expertise under tight
deadlines to improve each of the contributions.
Maria Cobb, University of Southern Mississippi
Hattiesburg, Mississippi USA
[e-mail]
Frederick Petry, Tulane University
New Orleans, Louisiana USA
[e-mail]
Vince Robinson, University of Toronto
Mississauga, Ontario Canada
[e-mail]
September 2, 2004
Contents
Foreword............................................................................................................v
Preface.............................................................................................................vii
Reasoning About Regions, Relations, and Fields
1. Fuzzy Reasoning about Geographic Regions
Hans W. Guesgen...........................................................................................1
2. Combined Extraction of Directional and Topological Relationship
Information from 2D Concave Objects
Pascal Matsakis and Dennis Nikitenko.......................................................15
3. Field Based Methods for the Modeling of Fuzzy Spatial Data
Jörg Verstraete, Guy De Tré, Rita De Caluwe and Axel Hallez.................41
4. Modeling Localities with Fuzzy Sets and GIS
Sungsoon Hwang and Jean-Claude Thill...................................................71
Fuzzy Classification
5. Mining Weather Data Using Fuzzy Cluster Analysis
Zhijian Liu and Roy George..................................................................... 105
6. Modelling the Fuzzy Spatial Extent of Geographical Entities
Cidália Costa Fonte and Weldon A. Lodwick...........................................121
7. Multi-Dimensional Interpolations with Fuzzy Sets
Suzana Dragi(cid:252)evi(cid:252)....................................................................................143
8. Talking Space – A Social & Fuzzy Logical GIS Perspective on
Modelling Spatial Dynamics
Susanne Kratochwil and Josef Benedikt...................................................159
9. A Valuation of the Reliability of a GIS Based on the Fuzzy Logic
in a Concrete Case Study
Ferdinando Di Martino, Vincenzo Loia, Salvatore Sessa,
and Michele Giordano..............................................................................185
Fuzzy Representations of Landscape Features
10. Fuzziness and Ambiguity in Multi-Scale Analysis of Landscape
Morphometry
Peter Fisher, Jo Wood, and Tao Cheng....................................................209
11. Fuzzy Representation of Special Terrain Features Using a
Similarity-based Approach
Xun Shi, A-Xing Zhu, and Rongxun Wang................................................233
Decision Making with GIS and Fuzzy Sets
12. Spatial Decision-Making Using Fuzzy Decision Tables: Theory,
Application and Limitations
Frank Witlox and Ben Derudder...............................................................253
13. Spatial Decision Making Using Fuzzy GIS
Ashley Morris and Piotr Jankowski..........................................................275
14.Spatially Explicit Individual-Based Ecological Modeling with
Mobile Fuzzy Agents
Vincent B. Robinson and Phil A. Graniero...............................................299
Index.................................................................................................................335
1. Fuzzy Reasoning about Geographic Regions
HansWernerGuesgen
ComputerScienceDepartment,UniversityofAuckland
PrivateBag92019,Auckland,NewZealand
[e-mail]
Abstract. Reasoningaboutgeographicregions,likeforests,lakes,cities,etc.,ofteninvolves
uncertaintyandimprecision.Forexample,whenwetalkaboutaregionlikethecityofAuck-
land,weusuallydonotknowexactlytheboundariesofthatregion.Nevertheless,weareable
toreasonaboutsucharegion.Orifwehearontheradiothatacoldfrontismovinginfrom
Antarctica,wecanestimatewhenitwillreachNewZealand,althoughwemightnotbeable
todeterminewithcertaintytheexactrelationbetweentheareacoveredbythecoldfrontand
theonethatisreferredtoasNewZealand.
Recently,theRCCtheoryhasgainedaparticularinterestintheAIresearchcommunity
asformalismtoreasonaboutregions.Thisfirst-ordertheoryisbasedonaprimitiverelation,
calledconnectedness, anduseseighttopological relations,definedonthebasisofconnect-
edness,toprovideaframeworktoreasonaboutregions.LehmannandCohnhaveintroduced
anextensiontotheRCCtheory,whichdealswithimprecisioninspatialrepresentations.Our
workcarriesonfromtherebyapplyingfuzzysetstotheRCCtheoryandintroducingauni-
formframeworktoreasonaboutgeographicregionsunderuncertaintyandimprecision.
1.1. Introduction
Inthelasttwodecades,theamountofworkonformalismsbasedonspatialrelations
hasincreasedsteadily.EarlyapproachesmainlyusedextensionsofAllen’sinterval
algebra(Allen,1983)forreasoningaboutspace.In(GuesgenandHertzberg,1993),
forexample,weintroduceaformofspatialreasoningthatextendsAllen’srelations
tothethreedimensionsofspacebyapplyingverysimplemethodsforconstructing
higher-dimensionalmodels and for reasoning about them. Freksa (1990) uses the
samesetofrelationsandshowsthatforanimportantclassofproblems,onlyasmall
subset of all possible combinations of spatial relations can occur. By restricting
himselftosetsofconceptuallyneighboringrelations,hecanrestrictthecomplexity
oftheconstraintsatisfactionalgorithmssignificantly.
Herna´ndez(1991)introducesanextensionofAllen’sapproachtorepresentthe
spatialfeaturesoccurringin2Dprojectionsof3Dscenes.Hesuggeststoestablish
spatial relations between objects by splitting them up into two aspects: projection
andorientation.MukerjeeandJoe’swork(1990)issimilartoHerna´ndez’sapproach.
Objectsofatwo-dimensionalworldarecharacterizedbythedirectionsinwhichthe
objectsaremovingandbyassociatingwiththeobjectstrajectoriesalongwhichthey
aremoving.
KettaniandMoulin(1999)usethenotionofspatialconceptualmapstogenerate
anddescriberoutesinaqualitativeway.Theirspatialmodelsarebasedonthenotion
2 HGuesgen
ofobjectinfluenceareas.Theseareasdeterminehowpeoplereasonaboutobjects,
evaluatemetricmeasures,qualifydistancesbetweenobjects,etc.Mustoetal.(2000)
alsouseaqualitativeapproachtodescriberoutes(orcoursesofmotion,astheycall
them). They use qualitative motion vectors to abstract from irrelevantdetails of a
courseofmotion.
Recently,theRCCtheory(Randelletal.,1992)hasgainedaparticularinterest
intheAIresearchcommunityasformalismtoreasonaboutregions.Thisfirst-order
theoryis based on a primitiverelation,called connectedness,and uses eighttopo-
logical relations, defined on the basis of connectedness, to provide a framework
to reason aboutregions.Lehmannand Cohn (Lehmannand Cohn, 1994)have in-
troduced an extension to the RCC theory,which deals with imprecision in spatial
representations. Our own work (Guesgen, 2002, 2003) carries on from this work
byintroducingfuzzysetsintotheRCCtheory.Thischapterbuildsonourprevious
results and introduces a uniform framework based on fuzzy sets to reason about
geographicregionsunderuncertaintyandimprecision.
1.2. The RCC Theory
Theideaofusingrelationstoreasonaboutspatio-temporalinformationdatesback
at least to the beginningof the eighties, whenAllen (1983)introducedan interval
logic for reasoningaboutrelationsbetweentime intervals.AlthoughAllen’s logic
canbeusedtoreasonabouttwo-dimensionalspace(Guesgen,1989),itoftenleads
to counterintuitiveresults. For example, consider two rectangular-shapedregions,
one of which is not aligned to the reference axes (see Figure 1.1). Using Allen’s
(cid:3) (cid:1)
(cid:2)
(cid:2) (cid:3)
(cid:3) (cid:3)
(cid:3) (cid:3) (cid:2)
(cid:3) (cid:3)
(cid:1)(cid:1)(cid:0)(cid:2)(cid:1) (cid:3) (cid:1) (cid:3)
(cid:3) (cid:3)
(cid:3) (cid:3)
(cid:3) (cid:3)
(cid:3) (cid:3)
(cid:2)
(cid:3)(cid:2)
(cid:0)
(cid:0)
(cid:1)(cid:0)(cid:0)(cid:2)(cid:0)
Fig.1.1.Therelationsbetweentworectangleswithrespecttothe -axisand -axis,where
denotestheAllenrelation . (cid:0) (cid:3) (cid:0)
(cid:0)(cid:1)(cid:2)(cid:3)(cid:4)(cid:5)
relationstodescribetherelationshipsbetweentheprojectionsoftherectangleson