Table Of ContentAdvanced Information and Knowledge Processing
SeriesEditors
ProfessorLakhmiJain
[email protected]
ProfessorXindongWu
[email protected]
Forothertitlespublishedinthisseries,goto
www.springer.com/series/4738
Chenyi Hu Ralph Baker Kearfott
•
Andre´ de Korvin Vladik Kreinovich
•
Editors
Knowledge Processing
with Interval and Soft
Computing
123
Editors
ChenyiHu RalphBakerKearfott
ComputerScienceDepartment MathematicsDepartment
UniversityofCentralArkansas UniversityofLouisiana,USA
Conway,Arkansas,USA
Andre´deKorvin VladikKreinovich
ComputerandMathematicalSciences ComputerScienceDepartment
Department UniversityofTexas,USA
UniversityofHouston-Downtown,USA
AI&KPISSN1610-3947
ISBN:978-1-84800-325-5 e-ISBN:978-1-84800-326-2
DOI:10.1007/978-1-84800-326-2
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Preface
Modern technologies have collected massive datasets from observations, ex-
periments,andscientificsimulation.Althoughprogresshasbeenmade,itstill
remainsachallengetoeffectivelyandefficientlydiscoverknowledgefromsuch
massive datasets. This is mainly because of the following two features. One
is that the size and number of attributes (dimensions) of some datasets can
be unmanageable. The other is that, due to the dynamic nature of the real
world, changes and uncertainties are characteristics of datasets.
A significant change in scientists’ ability to analyze data to obtain
a better understanding of natural phenomena will be enabled by (i)
new ways to manage massive amounts of data from observations and
scientificsimulation,(ii)integrationofpowerfulanalysistoolsdirectly
into the database,
···
Final report of the International Science 2020 Group, Microsoft, 2006
In contrast to classical point methods for arranging and processing data,
in this book, we investigate strategies for knowledge processing with interval
and soft computing.
Knowledge processing with interval methods has intrinsic merit. First,
qualitative properties are often presented as ranges of data attributes rather
thanspecificpoints.Forexample,one’sbloodpressureisnormalifwithinthe
normal range (i. e. normal interval). By grouping attribute values into mean-
ingful intervals, we can omit insignificant quantitative differences and focus
more on qualitatively processing datasets. More importantly, interval-valued
attributescontainmoreinformationthanpointsandcanrepresentvariability
and uncertainty. Finally, interval-valued computational results can be more
meaningful and useful than point-valued output in a dynamic environment.
Statistical and probabilistic methods have been widely applied in knowl-
edge discovery. However, despite the fact that confidence intervals and fuzzy
intervalshavebeenusedtodealwithuncertainties,theymaynotalwayswork
VI Preface
well in practice. By integrating interval methods with stochastic models and
fuzzy logic, this book provides at least additional, if not more powerful, tools
for knowledge processing, especially for handling variability and uncertainty.
Successful applications have been putting interval computing into the
mainstream of computing. In 2006, the C++ standard committee evaluated
a detailed proposal to include interval computing as a part of the ANSI/ISO
C++ standard library. Interval arithmetic has already been in the kernel
computations of Intel’s Itanium-based architecture. Aside from many other
software tools, Sun Microsystems has already included interval arithmetic in
its Sun Studio.
More importantly, applying unique properties of interval computing, new
algorithms have been developed to solve some otherwise very difficult prob-
lems. For example, one can computationally find all roots for nonlinear sys-
tems of equations on a given domain with interval Newton/generalized bisec-
tion methods and reliably find nonlinear global optima with interval branch-
and-bound algorithms computationally. Very recently, Ferguson and Hales
proved the 400-year-old Kepler conjecture with interval methods. In 2007,
they received the first Robbins Prize from American Mathematical Society
for their work.
Knowledge processing with intervals is significantly different from that
withpoints.Inthisbook,weextendpreviousknowledgeprocessingmethodsto
interval-valued datasets. By embedding interval and soft computing methods
into distributed homogeneous and/or heterogeneous database systems that
collectandmanagemassivedatasets,scientistsmaysignificantlyenhancetheir
ability to process massive datasets.
Thisbookcanbeusedasanintroductiontointervalmethodsandsoftcom-
puting for knowledge processing for upper-level undergraduates or first-year
graduatestudents.Itcanalsobeareferenceforresearchersandpractitioners.
We intended to make this book self-contained. Chapters 1, 2, and 3 pro-
vide necessary background knowledge for readers who are unfamiliar with
interval and soft computing. Specifically, Chapter 1 introduces fundamentals
of interval computing. In using interval computing for knowledge processing,
soft computing technologies are applied. Therefore, Chapter 2 reviews essen-
tialsofsoftcomputing.Althoughintervalarithmeticandsoftcomputingwere
developed independently, both of them can deal with uncertainty. We devote
Chapter3topresentingtheirrelationships.Readersfamiliarwiththesetopics
may skip the first three chapters.
Innovative algorithms and applications of interval and soft computing in
knowledge processing are reported in Chapters 4 to 9. Specifically, Chapter 4
discusses knowledge processing methods related to interval linear algebra.
Chapter 5 investigates interval function approximation. Chapter 6 presents
an interval decision-making system. Chapter 7 studies interval-valued ma-
trix games. Chapter 8 extends graph algorithms for interval-weighted graphs.
Chapter 9 uses intervals in probabilistic studies. In Chapter 10, we present a
standards-basedobject-orientedintervalcomputingenvironmentinC++.The
Preface VII
entire software package is available at http://www.cs.uca.edu/interval/.
Althoughtheseindependentchapterscoverdifferenttopics,thereissomeover-
lap. Each chapter is self-contained, but we reference other chapters as appro-
priate. By collecting our research results into a single volume, we unify and
make accessible previously published work.
This book only introduces some initial applications of interval methods in
knowledge processing. We sincerely hope to see more fruitful and significant
results in both of theory and application in the future.
We would like to express our great appreciations to all co-authors of
this volume. Hu, especially, would also like to acknowledge the US National
Science Foundation for the grant awards of NSF/CISE/CCF-0202042 and
NSF/CISE/CCF-0727798.
University of Central Arkansas, Conway, USA Chenyi Hu
University of Louisiana, Lafayette, USA Ralph Baker Kearfott
University of Houston-Downtown, Houston, USA Andr´e de Korvin
University of Texas, El Paso, USA Vladik Kreinovich
Contents
Preface ........................................................ V
List of Contributors ........................................... XI
1 Fundamentals of Interval Computing
Ralph Baker Kearfott, Chenyi Hu .................................. 1
2 Soft Computing Essentials
Andre de Korvin, Hong Lin, and Plamen Simeonov .................. 13
3 Relations Between Interval Computing and Soft Computing
Vladik Kreinovich................................................ 75
4 Interval Matrices in Knowledge Discovery
Chenyi Hu, R. Baker Kearfott ..................................... 99
5 Interval Function Approximation and Applications
Chenyi Hu, Ling T. He, Shanying Xu ..............................119
6 Interval Rule Matrices for Decision Making
Chenyi Hu ......................................................135
7 Interval Matrix Games
W. Dwayne Collins, Chenyi Hu....................................147
8 Interval-Weighted Graphs and Flow Networks
Chenyi Hu, Ping Hu..............................................167
9 Arithmetic on Bounded Families of Distributions: A DEnv
Algorithm Tutorial
Daniel Berleant, Gary Anderson, Chaim Goodman-Strauss ............183
X Contents
10 IntBox: An Object-Oriented Interval Computing Software
Toolbox in C++
Michael Nooner, Chenyi Hu .......................................211
Index..........................................................229
List of Contributors
Chenyi Hu Daniel Berleant
University of Central Arkansas UniversityofArkansasatLittleRock
201 Donaghey Avenue 2801 S. University Avenue
Conway, AR 72035, USA Little Rock, AR 72204, USA
[email protected] [email protected]
W. Dwayne Collins
Ralph Baker Kearfott Hendrix College
University of Louisiana at Lafayette 1600 Washington Avenue
Box 4-1010 Conway, AR 72032, USA
Lafayette, LA 70504-1010, USA [email protected]
[email protected] Chaim Goodman-Strauss
UniversityofArkansasatFayetteville
Andre de Korvin Fayetteville, AR 72701, USA
University of Houston-Downtown [email protected]
One Main Street Ling T. He
Houston, TX 77002, USA University of Central Arkansas
[email protected] 201 Donaghey Avenue
Conway, AR 72035, USA
Vladik Kreinovich [email protected]
University of Texas at El Paso Ping Hu
500 W. University University of Central Arkansas
El Paso, TX 79968, USA 201 Donaghey Avenue
[email protected] Conway, AR 72035, USA
[email protected]
Gary Anderson Hong Lin
UniversityofArkansasatLittleRock University of Houston-Downtown
2801 S. University Avenue One Main Street
Little Rock, AR 72204, USA Houston, TX 77002, USA
[email protected] [email protected]
