Leonid S. Bershtein (Taganrog Technological Institute of Southern Federal University, Russia) and Alexander V. Bozhenyuk (Taganrog Technological Institute of Southern Federal University, Russia)

DOI: 10.4018/978-1-59904-849-9.ch105

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TopThis article presents the main notations of fuzzy graphs and fuzzy hypergraphs, invariants of fuzzy graphs and hypergraphs.

Multiarity Relation: A multiarity relation R between elements of sets A, B, …, C is a subset of A×B×…×C.

Binary Relation: A binary relation R from a set A to a set B is a subset of A×B.

Isomorphic Graphs: Two graphs that have a structure-preserving vertex bijection between them.

Graph Invariant: A property of a graph that is preserved by isomorphisms.

Graph: A graph G = (V, E) is a mathematical structure consisting of two finite sets V and E. The elements of V are called vertices (or nodes), and the elements of E are called edges. Each edge has a set of one or two vertices associated to it, which are called its endpoints.

Binary Symmetric Relation: A relation R on a set A is symmetric if for all x,y?A xRy?yRx.

Fuzzy Set: A generalization of the definition of the classical set. A fuzzy set is characterized by a membership function, which maps the member of the universe into the unit interval, thus assigning to elements of the universe degrees of belongingness with respect to a set.

Membership Function: The membership function of a fuzzy set is a generalization of the characteristic function of crisp sets.

Hypergraph: A hypergraph on a finite set X={x1,x2,…,xn} is a family H={E1,E2,…,Em} of subsets of X such that Ei ? Ø and and .

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Chapter 5

Adaptive Neuro-Fuzzy Systems
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Agent-Based Intelligent System Modeling
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AI Methods for Analyzing Microarray Data
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Chapter 11

An AI Walk from Pharmacokinetics to Marketing
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Algorithms for Association Rule Mining
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Vasudha Bhatnagar, Anamika Gupta, Naveen Kumar

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Analytics for Noisy Unstructured Text Data I
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Analytics for Noisy Unstructured Text Data II
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L. Venkata Subramaniam, Shourya Roy

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Chapter 17

Angiographic Images Segmentation Techniques
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Francisco J. Nóvoa, Alberto Curra, M. Gloria López, Virginia Mato

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Chapter 18

ANN Application in the Field of Structural Concrete
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Juan L. Pérez, Mª Isabel Martínez, Manuel F. Herrador

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ANN-Based Defects' Diagnosis of Industrial Optical Devices
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Artificial Intelligence and Rubble-Mound Breakwater Stability
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Artificial Intelligence in Computer-Aided Diagnosis
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Artificial NeuroGlial Networks
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Ana Belén Porto Pazos, Alberto Alvarellos González, Félix Montañés Pazos

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Chapter 30

Automatic Classification of Impact-Echo Spectra I
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Addisson Salazar, Arturo Serrano

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Automatic Classification of Impact-Echo Spectra II
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Addisson Salazar, Arturo Serrano

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AVI of Surface Flaws on Manufactures I
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Girolamo Fornarelli, Antonio Giaquinto

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AVI of Surface Flaws on Manufactures II
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Behaviour-Based Clustering of Neural Networks
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María José Castro-Bleda, Slavador España-Boquera, Francisco Zamora-Martínez

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Chapter 37

Bio-Inspired Algorithms in Bioinformatics I
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José Antonio Seoane Fernández, Mónica Miguélez Rico

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Chapter 38

Bio-Inspired Algorithms in Bioinformatics II
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José Antonio Seoane Fernández, Mónica Miguélez Rico

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Chapter 40

Bio-Inspired Dynamical Tools for Analyzing Cognition
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Manuel G. Bedia, Juan M. Corchado, Luis F. Castillo

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Class Prediction in Test Sets with Shifted Distributions
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Óscar Pérez, Manuel Sánchez-Montañés

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Cluster Analysis of Gene Expression Data
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Alan Wee-Chung Liew, Ngai-Fong Law, Hong Yan

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Chapter 47

CNS Tumor Prediction Using Gene Expression Data Part I
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CNS Tumor Prediction Using Gene Expression Data Part II
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Chapter 49

Combining Classifiers and Learning Mixture-of-Experts
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Chapter 53

A Comparison of Cooling Schedules for Simulated Annealing
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Chapter 54

Complex Systems Modeling by Cellular Automata
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Chapter 56

Component Analysis in Artificial Vision
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Oscar Déniz Suárez, Gloria Bueno García

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Chapter 58

Computer Morphogenesis in Self-Organizing Structures
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Enrique Fernández-Blanco, Julián Dorado de la Calle

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Chapter 59

Computer Vision for Wave Flume Experiments
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Conditional Hazard Estimating Neural Networks
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Antonio Eleuteri, Azzam Taktak, Bertil Damato, Angela Douglas, Sarah Coupland

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Continuous ACO in a SVR Traffic Forecasting Model
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Data Mining Fundamental Concepts and Critical Issues
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Data Warehousing Development and Design Methodologies
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Decision Tree Applications for Data Modelling
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Device-Level Majority von Neumann Multiplexing
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Chapter 73

Different Approaches for Cooperation with Metaheuristics
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Chapter 79

EA Multi-Model Selection for SVM
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Chapter 80

EC Techniques in the Structural Concrete Field
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Chapter 81

E-Learning in New Technologies
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Chapter 82

Emerging Applications in Immersive Technologies
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Chapter 83

Emulating Subjective Criteria in Corpus Validation
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Chapter 84

Energy Minimizing Active Models in Artificial Vision
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Chapter 85

Ensemble of ANN for Traffic Sign Recognition
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Chapter 86

Ensemble of SVM Classifiers for Spam Filtering
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Chapter 87

Evolutionary Algorithms in Discredibility Detection
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Evolutionary Approaches for ANNs Design
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Evolutionary Approaches to Variable Selection
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Evolutionary Computing Approach for Ad-Hoc Networks
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Chapter 91

Evolutionary Grammatical Inference
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Evolved Synthesis of Digital Circuits
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Chapter 94

Evolving Graphs for ANN Development and Simplification
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Chapter 95

Facial Expression Recognition for HCI Applications
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Chapter 98

Finding Multiple Solutions with GA in Multimodal Problems
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Chapter 100

Functional Dimension Reduction for Chemometrics
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Chapter 101

Functional Networks
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Chapter 102

Fuzzy Approximation of DES State
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Chapter 105

Fuzzy Graphs and Fuzzy Hypergraphs
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Chapter 106

Fuzzy Logic Applied to Biomedical Image Analysis
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Chapter 107

Fuzzy Logic Estimator for Variant SNR Environments
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Chapter 110

Gene Regulation Network Use for Information Processing
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Chapter 113

Genetic Fuzzy Systems Applied to Ports and Coasts Engineering
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Chapter 114

Grammar-Guided Genetic Programming
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Chapter 116

Growing Self-Organizing Maps for Data Analysis
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Chapter 117

GTM User Modeling for aIGA Weight Tuning in TTS Synthesis
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Chapter 118

Handling Fuzzy Similarity for Data Classification
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Roy Gelbard, Avichai Meged

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Chapter 120

Hierarchical Neuro-Fuzzy Systems Part I
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Chapter 121

Hierarchical Neuro-Fuzzy Systems Part II
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Marley Vellasco, Marco Pacheco, Karla Figueiredo, Flavio Souza

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Chapter 123

High Level Design Approach for FPGA Implementation of ANNs
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Nouma Izeboudjen, Ahcene Farah, Hamid Bessalah, Ahmed Bouridene, Nassim Chikhi

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Chapter 124

HOPS: A Hybrid Dual Camera Vision System
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Stefano Cagnoni, Monica Mordonini, Luca Mussi, Giovanni Adorni

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Chapter 125

Hybrid Dual Camera Vision Systems
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Chapter 126

Hybrid Meta-Heuristics Based System for Dynamic Scheduling
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Ana Maria Madureira

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Chapter 127

A Hybrid System for Automatic Infant Cry Recognition I
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Carlos Alberto Reyes-García, Ramon Zatarain, Lucia Barron, Orion Fausto Reyes-Galaviz

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Chapter 128

A Hybrid System for Automatic Infant Cry Recognition II
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Carlos Alberto Reyes-García, Sandra E. Barajas, Esteban Tlelo-Cuautle, Orion Fausto Reyes-Galaviz

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Chapter 134

Intelligent Classifier for Atrial Fibrillation (ECG)
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O. Valenzuela, I. Rojas, F. Rojas, A. Guillen, L. J. Herrera, F. J. Rojas, M. Cepero

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Chapter 135

Intelligent MAS in System Engineering and Robotics
(pages 917-923)

G. Nicolás Marichal, Evelio J. González

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Chapter 136

Intelligent Query Answering Mechanism in Multi Agent Systems
(pages 924-932)

Safiye Turgay, Fahrettin Yaman

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Chapter 137

Intelligent Radar Detectors
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Raúl Vicen Bueno, Manuel Rosa Zurera, María Pilar Jarabo Amores, Roberto Gil Pita, David de la Mata Moya

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Chapter 138

Intelligent Software Agents Analysis in E-Commerce I
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Xin Luo, Somasheker Akkaladevi

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Chapter 139

Intelligent Software Agents Analysis in E-Commerce II
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Xin Luo, Somasheker Akkaladevi

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Chapter 140

Intelligent Software Agents with Applications in Focus
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Mario Jankovic-Romano, Milan Stankovic, Uroš Krcadinac

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Chapter 141

Intelligent Traffic Sign Classifiers
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Raúl Vicen Bueno, Elena Torijano Gordo, Antonio García González, Manuel Rosa Zurera, Roberto Gil Pita

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Chapter 143

Intuitionistic Fuzzy Image Processing
(pages 967-974)

Ioannis K. Vlachos, George D. Sergiadis

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Chapter 144

Knowledge Management Systems Procedural Development
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Javier Andrade, Santiago Rodríguez, María Seoane, Sonia Suárez

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Chapter 145

Knowledge Management Tools and Their Desirable Characteristics
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Juan Ares, Rafael García, María Seoane, Sonia Suárez

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Chapter 147

Kohonen Maps and TS Algorithms
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Marie-Thérèse Boyer-Xambeu, Ghislain Deleplace, Patrice Gaubert, Lucien Gillard

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Chapter 148

Learning in Feed-Forward Artificial Neural Networks I
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Lluís A. Belanche Muñoz

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Chapter 149

Learning in Feed-Forward Artificial Neural Networks II
(pages 1012-1017)

Lluís A. Belanche Muñoz

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Chapter 151

Learning-Based Planning
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Sergio Jiménez Celorrio, Tomás de la Rosa Turbides

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Chapter 152

A Longitudinal Analysis of Labour Market Data with SOM
(pages 1029-1035)

Patrick Rousset, Jean-Francois Giret

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Chapter 154

Many-Objective Evolutionary Optimisation
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Francesco di Pierro, Soon-Thiam Khu, Dragan A. Savic

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Chapter 155

Mapping Ontologies by Utilising Their Semantic Structure
(pages 1049-1055)

Yi Zhao, Wolfgang A. Halang

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Chapter 157

Microarray Information and Data Integration Using SAMIDI
(pages 1064-1071)

Juan M. Gómez, Ricardo Colomo, Marcos Ruano, Ángel García

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Chapter 158

Mobile Robots Navigation, Mapping, and Localization Part I
(pages 1072-1079)

Lee Gim Hee, Marcelo H. Ang Jr.

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Chapter 159

Mobile Robots Navigation, Mapping, and Localization Part II
(pages 1080-1088)

Lee Gim Hee, Marcelo H. Ang Jr.

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Chapter 160

Modal Logics for Reasoning about Multiagent Systems
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Nikolay V. Shilov, Natalia Garanina

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Chapter 161

Modularity in Artificial Neural Networks
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Ricardo Téllez, Cecilio Angulo

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Chapter 163

MREM, Discrete Recurrent Network for Optimization
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Enrique Mérida-Casermeiro, Domingo López-Rodríguez, Juan M. Ortiz-de-Lazcano-Lobato

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Chapter 164

Multilayer Optimization Approach for Fuzzy Systems
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Chapter 166

Multilogistic Regression by Product Units
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Chapter 167

Multi-Objective Evolutionary Algorithms
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Chapter 168

Multi-Objective Training of Neural Networks
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Chapter 171

Natural Language Processing and Biological Methods
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Gemma Bel Enguix, M. Dolores Jiménez López

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Chapter 172

Natural Language Understanding and Assessment
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Chapter 175

Neural Control System for Autonomous Vehicles
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Chapter 176

Neural Network-Based Visual Data Mining for Cancer Data
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Chapter 178

Neural Networks and Equilibria, Synchronization, and Time Lags
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Chapter 179

Neural Networks and HOS for Power Quality Evaluation
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Chapter 180

Neural Networks on Handwritten Signature Verification
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Chapter 182

A New Self-Organizing Map for Dissimilarity Data
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Chapter 183

NLP Techniques in Intelligent Tutoring Systems
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Chapter 184

Non-Cooperative Facial Biometric Identification Systems
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Chapter 185

Nonlinear Techniques for Signals Characterization
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Chapter 186

Ontologies and Processing Patterns for Microarrays
(pages 1273-1277)

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Chapter 187

Ontologies for Education and Learning Design
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Chapter 188

Ontology Alignment Overview
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Chapter 189

Ontology Alignment Techniques
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Chapter 190

Optimization of the Acoustic Systems
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Chapter 191

Particle Swarm Optimization and Image Analysis
(pages 1303-1309)

Stefano Cagnoni, Monica Mordonini

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Chapter 193

Planning Agent for Geriatric Residences
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Chapter 194

Privacy-Preserving Estimation
(pages 1323-1329)

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Chapter 195

Protein Structure Prediction by Fusion,Bayesian Methods
(pages 1330-1336)

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Chapter 196

Prototype Based Classification in Bioinformatics
(pages 1337-1342)

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Chapter 199

RBF Networks for Power System Topology Verification
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Chapter 200

Representing Non-Rigid Objects with Neural Networks
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Chapter 201

A Roadmap on Updates
(pages 1370-1375)

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Chapter 202

A Robot Model of Dynamic Appraisal and Response
(pages 1376-1382)

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Chapter 206

Rule Engines and Agent-Based Systems
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Chapter 207

Sequence Processing with Recurrent Neural Networks
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Chun-Cheng Peng, George D. Magoulas

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Chapter 208

Shortening Automated Negotiation Threads via Neural Nets
(pages 1418-1425)

Ioanna Roussaki, Ioannis Papaioannou, Miltiades Anagnostou

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Chapter 209

Signed Formulae as a New Update Process
(pages 1426-1432)

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Chapter 210

Solar Radiation Forecasting Model
(pages 1433-1438)

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Chapter 211

Speech-Based Clinical Diagnostic Systems
(pages 1439-1446)

Jesús Bernardino Alonso Hernández, Patricia Henríquez Rodríguez

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Chapter 212

State of the Art in Writer's Off-Line Identification
(pages 1447-1454)

Carlos M. Travieso González, Carlos F. Romero

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Chapter 213

State-of-the-Art on Video-Based Face Recognition
(pages 1455-1461)

Yan Yan, Yu-Jin Zhang

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Chapter 214

Stationary Density of Stochastic Search Processes
(pages 1462-1466)

Arturo Berrones, Dexmont Peña, Ricardo Sánchez

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Chapter 215

Statistical Modelling of Highly Inflective Languages
(pages 1467-1473)

Mirjam Sepesy Maucec, Zdravko Kacic

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Chapter 216

Statistical Simulations on Perceptron-Based Adders
(pages 1474-1481)

Snorre Aunet, Hans Kristian Otnes Berge

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Chapter 218

Stream Processing of a Neural Classifier I
(pages 1490-1496)

M. Martínez-Zarzuela, F. J. Díaz Pernas, D. González Ortega, J. F. Díez Higuera, M. Antón Rodríguez

$37.50

Chapter 219

Stream Processing of a Neural Classifier II
(pages 1497-1503)

M. Martínez-Zarzuela, F. J. Díaz Pernas, D. González Ortega, J. F. Díez Higuera, M. Antón Rodríguez

$37.50

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$37.50

Chapter 223

A Survey on Neural Networks in Automated Negotiations
(pages 1524-1529)

Ioannis Papaioannou, Ioanna Roussaki, Miltiades Anagnostou

$37.50

Chapter 224

Swarm Intelligence Approach for Ad-Hoc Networks
(pages 1530-1536)

Prayag Narula, Sudip Misra, Sanjay Kumar Dhurandher

$37.50

$37.50

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Chapter 230

Thermal Design of Gas-Fired Cooktop Burners Through ANN
(pages 1568-1575)

T. T. Wong, C. W. Leung

$37.50

Chapter 231

A 2D Positioning Application in PET Using ANNs
(pages 1576-1582)

Fernando Mateo, Ramón J. Aliaga, Jorge D. Martínez, José Ma Monzó, Rafael Gadea

$37.50

Chapter 232

2D-PAGE Analysis Using Evolutionary Computation
(pages 1583-1588)

Pablo Mesejo, Enrique Fernández-Blanco, Diego Martínez-Feijóo, Francisco J. Blanco

$37.50

Chapter 233

Visualizing Cancer Databases Using Hybrid Spaces
(pages 1589-1595)

Julio J. Valdés, Alan J. Barton

$37.50

Chapter 234

Voltage Instability Detection Using Neural Networks
(pages 1596-1602)

Adnan Khashman, Kadri Buruncuk, Samir Jabr

$37.50

Chapter 235

Wave Reflection at Submerged Breakwaters
(pages 1603-1609)

Alberte Castro Ponte, Gregorio Iglesias, Francisco Taveira Pinto, Rodrigo Carballo

$37.50

Chapter 236

Web-Based Assessment System Applying Many-Valued Logic
(pages 1610-1614)

Sylvia Encheva, Sharil Tumin

$37.50

Chapter 237

Workflow Management Based on Mobile Agent Technology
(pages 1615-1623)

Marina Flores-Badillo, Ernesto López-Mellado

$37.50

About the Editors

Index