Handbook of Granular Computing

by Pedrycz, Witold; Skowron, Andrzej; Kreinovich, Vladik

• ISBN13: 9780470035542
• ISBN10: 0470035544
• Edition: 1st
• Format: Hardcover
• Copyright: 2008-08-25
• Publisher: Wiley-Interscience

Summary

Although the notion is a relatively recent one, the notions and principles of Granular Computing (GrC) have appeared in a different guise in many related fields including granularity in Artificial Intelligence, interval computing, cluster analysis, quotient space theory and many others. Recent years have witnessed a renewed and expanding interest in the topic as it begins to play a key role in bioinformatics, e-commerce, machine learning, security, data mining and wireless mobile computing when it comes to the issues of effectiveness, robustness and uncertainty.The Handbook of Granular Computing offers a comprehensive reference source for the granular computing community, edited by and with contributions from leading experts in the field. Includes chapters covering the foundations of granular computing, interval analysis and fuzzy set theory; hybrid methods and models of granular computing; and applications and case studies. Divided into 5 sections: Preliminaries, Fundamentals, Methodology and Algorithms, Development of Hybrid Models and Applications and Case Studies. Presents the flow of ideas in a systematic, well-organized manner, starting with the concepts and motivation and proceeding to detailed design that materializes in specific algorithms, applications and case studies. Provides the reader with a self-contained reference that includes all pre-requisite knowledge, augmented with step-by-step explanations of more advanced concepts.The Handbook of Granular Computing represents a significant and valuable contribution to the literature and will appeal to a broad audience including researchers, students and practitioners in the fields of Computational Intelligence, pattern recognition, fuzzy sets and neural networks, system modelling, operations research and bioinformatics.

Author Biography

Witold Pedrycz is a Professor and Canada Research Chair (CRC) in the Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Canada. He is also with the Systems Research Institute of the Polish Academy of Sciences. He is actively pursuing research in Computational Intelligence, fuzzy modeling, knowledge discovery and data mining, fuzzy control including fuzzy controllers, pattern recognition, knowledge-based neural networks, relational computation, bioinformatics, and Software Engineering. He has published numerous papers in this area. He is also an author of 9 research monographs covering various aspects of Computational Intelligence and Software Engineering.

Andrzej Skowron holds a Ph.D. degree in Mathematical Foundations of Computer Science from the University of Warsaw in Poland, Doctor of Science (Habilitation) degree in Mathematical Foundations of Computer Science from the University of Warsaw in Poland. In 1991 he received the Scientific Title of Professor. Andrzej Skowron is the author and co-author of more than 280 scientific publications, 15 edited books and several special issues of international journals.

Vladik Kreinovich Department of Computer Science University of Texas. He received his M.S. in Mathematics and Computer Science from St. Petersburg University, Russia, in 1974, and Ph.D. from the Institute of Mathematics, Soviet Academy of Sciences, Published 6 books and more than 600 papers. Member of the editorial board of the international journal "Reliable Computing" (formerly, "Interval Computations"), and several other journals. Co-maintainer of the international website on interval computations.

Table of Contents

Preface

Foreword

Biographies

Fundamentals and Methodology of Granular Computing Based on Interval Analysis

Interval Computation as an Important Part of Granular Computing: An Introduction

Stochastic Arithmetic as a Model of Granular Computing

Fundamentals of Interval Analysis and Linkages to Fuzzy Set Theory

Interval Methods for Non-Linear Equation Solving Applications

Fuzzy Sets as a User-Centric Processing Framework of Granular Computing

Measurement and Elicitation of Membership Functions

Fuzzy Clustering as a Data-Driven Development Environment for Information Granules

Encoding and Decoding of Fuzzy Granules

Systems of Information Granules

Logical Connectives for Granular Computing

Calculi of Information Granules. Fuzzy Relational Equations

Fuzzy Numbers and Fuzzy Arithmetic

Rough-Granular Computing

Wisdom Granular Computing

Granular Computing for Reasoning about Ordered Data: The Dominance-Based Rough Set Approach

A Unified Approach to Granulation of Knowledge and Granular Computing Based on Rough Mereology: A Survey

A Unified Framework of Granular Computing

Quotient Spaces and Granular Computing

Rough Sets and Granular Computing: Toward Rough-Granular Computing

Construction of Rough Information Granules

Spatiotemporal Reasoning in Rough Sets and Granular Computing

Hybrid Methods and Models of Granular Computing

A Survey of Interval-Valued Fuzzy Sets

Measurement Theory and Uncertainty in Measurements: Application of Interval Analysis and Fuzzy Sets Methods

Fuzzy Rough Sets: From Theory into Practice

On Type 2 Fuzzy Sets as Granular Models for Words

Design of Intelligent Systems with Interval Type-2 Fuzzy Logic

Theoretical Aspects of Shadowed Sets

Fuzzy Representations of Spatial Relations for Spatial Reasoning

RoughGNeural Methodologies in Granular Computing

Approximation and Perception in Ethology-Based Reinforcement Learning

Fuzzy Linear Programming

A Fuzzy Regression Approach to Acquisition of Linguistic Rules

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