Foundations of Computational Intelligence Volume 2: Approximate Reasoning

323 Pages·2009·9.9 MB·English

by  James F. Peters (auth.)

Aboul-EllaHassanien,AjithAbraham,andFranciscoHerrera(Eds.)
FoundationsofComputationalIntelligenceVolume2
StudiesinComputationalIntelligence,Volume202
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Foundations of Computational
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Approximate Reasoning
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Preface

Foundations of Computational Intelligence

Volume 2: Approximation Reasoning: Theoretical Foundations and Applications

Human reasoning usually is very approximate and involves various types of un-
certainties. Approximate reasoning is the computational modelling of any part of
the process used by humans to reason about natural phenomena or to solve real
world problems. The scope of this book includes fuzzy sets, Dempster-Shafer
theory, multi-valued logic, probability, random sets, and rough set, near set and
hybrid intelligent systems. Besides research articles and expository papers on the-
ory and algorithms of approximation reasoning, papers on numerical experiments
and real world applications were also encouraged. This Volume comprises of 12
chapters including an overview chapter providing an up-to-date and state-of-the
research on the applications of Computational Intelligence techniques for ap-
proximation reasoning. The Volume is divided into 2 parts:

Part-I: Approximate Reasoning – Theoretical Foundations

Part-II: Approximate Reasoning – Success Stories and Real World Applications

Part I on Approximate Reasoning – Theoretical Foundations contains four chap-
ters that describe several approaches of fuzzy and Para consistent annotated logic
approximation reasoning.
In Chapter 1, “Fuzzy Sets, Near Sets, and Rough Sets for Your Computational
Intelligence Toolbox” by Peters considers how a user might utilize fuzzy sets, near
sets, and rough sets, taken separately or taken together in hybridizations as part of
a computational intelligence toolbox.
In multi-criteria decision making, it is necessary to aggregate (combine) utility
values corresponding to several criteria (parameters). The simplest way to com-
bine these values is to use linear aggregation. In many practical situations, how-
ever, linear aggregation does not fully adequately describe the actual decision
making process, so non-linear aggregation is needed. From the purely mathemati-
cal viewpoint, the next natural step after linear functions is the use of quadratic
VI Preface

functions. However, in decision making, a different type of non-linearities is
usually more adequate than quadratic ones: fuzzy-type non-linearities like OWA
or Choquet integral that use min and max in addition to linear combinations. In
Chapter 2, “Fuzzy Without Fuzzy: Why Fuzzy-Related Aggregation Techniques
Are Often Better Even in Situations Without True Fuzziness” by Nguyen et al.
gives a mathematical explanation for this empirical phenomenon. Specifically, the
authors show that approximation by using fuzzy methodology is indeed the best
(in some reasonable sense).
In Chapter 3, “Intermediate Degrees are needed for the World to be Cogniza-
ble: Towards a New Justification for Fuzzy Logic Ideas” Nguyen et al. prove
that intermediate degrees are needed to describe real-world processes and it pro-
vides an additional explanation for the success of fuzzy techniques (and other
techniques which use intermediate degrees) – which often goes beyond situations
in which the intermediate degrees are needed to describe the experts’ uncertainty.
Chapter 4, “Paraconsisitent annotated logic program Before After EVALSPN
and its applications” by Nakamatsu, proposes a paraconsistent annotated logic
program called EVALPSN. In EVALPSN, an annotation called an extended vec-
tor annotation is attached to each literal. In addition, the author introduces the bf-
EVALPSN and its application to real-time process order control and its safety
verification with simple examples.

Part II on Approximate Reasoning – Success Stories and Real World Applications
contains eight chapters that describe several success stories and real world appli-
cations on approximation reasoning.
In Chapter 5, “A Fuzzy Set Approach to Software Reliability Modeling”
Zeephongsekul provides a discussion of a fuzzy set approach, which is used to
extend the notion of software debugging from a 0-1 (perfect/imperfect) crisp ap-
proach to one which incorporates some fuzzy sets ideas.
Chapter 6, “Computational Methods for Investment Portfolio: the Use of Fuzzy
Measures and Constraint Programming for Risk Management” by Majoc et al.
present a state of the art on computational techniques for portfolio management,
that is, how to optimize a portfolio selection process and propose a novel approach
involving utility-based multi-criteria decision making setting and fuzzy integration
over intervals.
In Chapter 7, “A Bayesian Solution to the Modifiable Areal Unit Problem” Hui
explores how the Modifiable Areal Unit Problem (MAUP) can be described and
potentially solved by the Bayesian estimation (BYE). Specifically, the scale and
the aggregation problems are analyzed using simulated data from an individual-
based model.
In chapter 8, “Fuzzy Logic Control in Communication Networks” by Chry-
sostomou and Pitsillides discuss the difficulty of the congestion control problem
and review the control approaches currently in use. The authors motivate the util-
ity of Computational Intelligence based control and then through a number of ex-
amples, illustrate congestion control methods based on fuzzy logic control.
Preface VII

In Chapter 9, “Adaptation in Classification Systems” Bouchachia investigates
adaptation issues in learning classification systems from different perspectives.
Special attention is given to adaptive neural networks and the most visible incre-
mental learning mechanisms. Adaptation is also incorporated in the combination
of incremental classifiers in different ways so that adaptive ensemble learners are
obtained. These issues are illustrated by means of a numerical simulation.
In Chapter 10, “Music Instrument Estimation in Polyphonic Sound Based on
Short-Term Spectrum Match” Jiang et al. provide a new solution to an important
problem of instrument identification in polyphonic music: There is loss of infor-
mation on non-dominant instruments during the sound separation process due to
the overlapping of sound features. Experiments show that the sub-patterns
detected from the power spectrum slices contain sufficient information for the
multiple-timbre estimation tasks and improve the robustness of instrument identi-
fication.
In Chapter 11, “Ultrasound Biomicroscopy Glaucoma Images Analysis Based
on Rough Set and Pulse Coupled Neural Network” El-Dahshan et al. present
rough sets and pulse coupled neural network scheme for Ultrasound Biomicro-
scopy (UBM) glaucoma images analysis. The Pulse Coupled Neural Network
(PCNN) with a median filter was used to adjust the intensity of the UBM images.
This is followed by applying the PCNN-based segmentation algorithm to detect
the boundary of the interior chamber of the eye image. Then, glaucoma clinical
parameters are calculated and normalized, followed by application of a rough set
analysis to discover the dependency between the parameters and to generate set of
reducts that contains minimal number of attributes.
In Chapter 12, “An overview of fuzzy c-means based image clustering algo-
rithm” Huiyu Zhou and Gerald Schaefer provide an overview of several fuzzy c-
means based image clustering concepts and their applications. In particular, we
summarize the conventional fuzzy c-means (FCM) approaches as well as a num-
ber of its derivatives that aim at either speeding up the clustering process or at
providing improved or more robust clustering performance.
We are very much grateful to the authors of this volume and to the reviewers
for their great efforts by reviewing and providing interesting feedback to authors
of the chapter. The editors would like to thank Dr. Thomas Ditzinger (Springer
Engineering Inhouse Editor, Studies in Computational Intelligence Series),
Professor Janusz Kacprzyk (Editor-in-Chief, Springer Studies in Computational
Intelligence Series) and Ms. Heather King (Editorial Assistant, Springer Verlag,
Heidelberg) for the editorial assistance and excellent cooperative collaboration to
produce this important scientific work. We hope that the reader will share our joy
and will find it useful!

December 2008 Aboul Ella Hassanien, Cairo, Egypt
Ajith Abraham, Trondheim, Norway
Francisco Herrera, Granada, Spain

Contents
Part I: Approximate Reasoning - Theoretical Foundations and
Applications
Approximate Reasoning - Theoretical Foundations
Fuzzy Sets, Near Sets, and Rough Sets for Your
Computational Intelligence Toolbox ......................... 3
James F. Peters
Fuzzy without Fuzzy: Why Fuzzy-Related Aggregation
Techniques Are Often Better Even in Situations without
True Fuzziness............................................... 27
Hung T. Nguyen, Vladik Kreinovich, Franc¸ois Modave,
Martine Ceberio
Intermediate Degrees Are Needed for the World to Be
Cognizable: Towards a New Justification for Fuzzy Logic
Ideas ........................................................ 53
Hung T. Nguyen, Vladik Kreinovich, J. Esteban Gamez,
Fran¸cois Modave, Olga Kosheleva
Paraconsistent Annotated Logic Program Before-after
EVALPSN and Its Application .............................. 75
Kazumi Nakamatsu
Part II: Approximate Reasoning - Success Stories and Real World
Applications
A Fuzzy Set Approach to Software Reliability Modeling ..... 111
P. Zeephongsekul