Granular Computing: Analysis and Design of Intelligent Systems, 1st Edition (Paperback) book cover

Granular Computing

Analysis and Design of Intelligent Systems, 1st Edition

By Witold Pedrycz

CRC Press

309 pages | 154 B/W Illus.

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Information granules, as encountered in natural language, are implicit in nature. To make them fully operational so they can be effectively used to analyze and design intelligent systems, information granules need to be made explicit. An emerging discipline, granular computing focuses on formalizing information granules and unifying them to create a coherent methodological and developmental environment for intelligent system design and analysis. Granular Computing: Analysis and Design of Intelligent Systems presents the unified principles of granular computing along with its comprehensive algorithmic framework and design practices.

  • Introduces the concepts of information granules, information granularity, and granular computing
  • Presents the key formalisms of information granules
  • Builds on the concepts of information granules with discussion of higher-order and higher-type information granules
  • Discusses the operational concept of information granulation and degranulation by highlighting the essence of this tandem and its quantification in terms of the associated reconstruction error
  • Examines the principle of justifiable granularity
  • Stresses the need to look at information granularity as an important design asset that helps construct more realistic models of real-world systems or facilitate collaborative pursuits of system modeling
  • Highlights the concepts, architectures, and design algorithms of granular models
  • Explores application domains where granular computing and granular models play a visible role, including pattern recognition, time series, and decision making

Written by an internationally renowned authority in the field, this innovative book introduces readers to granular computing as a new paradigm for the analysis and synthesis of intelligent systems. It is a valuable resource for those engaged in research and practical developments in computer, electrical, industrial, manufacturing, and biomedical engineering. Building from fundamentals, the book is also suitable for readers from nontechnical disciplines where information granules assume a visible position.


"Dr. Pedrycz is an internationally acclaimed authority in the granular computing area. … I particularly appreciate his elegant writing style. This book is the first comprehensive treatise of the granular computing techniques and their application to the design of intelligent systems. … As an application-oriented practitioner in computational intelligence systems, I think that this book will be a welcome and strongly needed addition to this field. I cannot think of any other expert worldwide more qualified than Prof. Pedycz to write such a book."

—Emil M. Petriu, University of Ottawa, Canada

"This volume covers most of the interesting and important topics in granular computing. The contents may be well understood by senior or master course students in the field of computer science … also a good textbook for engineers who are involved in developing so-called intelligent systems."

—Kaoru Hirota, Tokyo Institute of Technology, Japan

"Dr. Pedrycz’s latest magnum opus … breaks new ground in many directions. [It] takes an important step toward achievement of human-level machine intelligence—a principal goal of artificial intelligence (AI) since its inception. … [This is] a remarkably well put together and reader-friendly collection of concepts and techniques, which constitute granular computing. … [The book] combines extraordinary breadth with extraordinary depth. It contains a wealth of new ideas, and unfolds a vast panorama of concepts, methods, and applications. … Dr. Pedrycz’s development and description of these concepts, techniques, and their applications is a truly remarkable achievement. … must reading for all who are concerned with the design and application of intelligent systems."

—From the Foreword by Lotfi A. Zadeh, University of California, Berkeley, USA

Table of Contents

Information Granularity, Information Granules, and Granular Computing

Information Granularity and the Discipline of Granular Computing

Formal Platforms of Information Granularity

Information Granularity and Its Quantification

Information Granules and a Principle of the Least Commitment

Information Granules of Higher Type and Higher Order

Hybrid Models of Information Granules

A Design of Information Granules

The Granulation–Degranulation Principle

Information Granularity in Data Representation and Processing

Optimal Allocation of Information Granularity

Key Formalisms for Representation of Information Granules and Processing Mechanisms

Sets and Interval Analysis

Interval Analysis

Fuzzy Sets: A Departure from the Principle of Dichotomy

Rough Sets

Shadowed Sets as a Three-Valued Logic Characterization of Fuzzy Sets

Information Granules of Higher Type and Higher Order, and Hybrid Information Granules

Fuzzy Sets of Higher Order

Rough Fuzzy Sets and Fuzzy Rough Sets

Type-2 Fuzzy Sets

Interval-Valued Fuzzy Sets

Probabilistic Sets

Hybrid Models of Information Granules: Probabilistic and Fuzzy Set Information Granules

Realization of Fuzzy Models with Information Granules of Higher Type and Higher Order

Representation of Information Granules

Description of Information Granules by a Certain Vocabulary of Information Granules

Information Granulation–Degranulation Mechanism in the Presence of Numeric Data

Granulation–Degranulation in the Presence of Triangular Fuzzy Sets

The Design of Information Granules

The Principle of Justifiable Granularity

Construction of Information Granules through Clustering of Numeric Experimental Evidence

Knowledge-Based Clustering: Bringing Together Data and Knowledge

Refinement of Information Granules through Successive Clustering

Collaborative Clustering and Higher-Level Information Granules

Optimal Allocation of Information Granularity: Building Granular Mappings

From Mappings and Models to Granular Mappings and Granular Models

Granular Mappings

Protocols of Allocation of Information Granularity

Design Criteria Guiding the Realization of the Protocols for Allocation of Information Granularity

Granular Neural Networks as Examples of Granular Nonlinear Mappings

Further Problems of Optimal Allocation of Information Granularity

Granular Description of Data and Pattern Classification

Granular Description of Data—A Shadowed Sets Approach

Building Granular Representatives of Data

A Construction of Granular Prototypes with the Use of the Granulation–Degranulation Mechanism

Information Granularity as a Design Asset and Its Optimal Allocation

Design Considerations

Pattern Classification with Information Granules

Granular Classification Schemes

Granular Models: Architectures and Development

The Mechanisms of Collaboration and Associated Architectures

Realization of Granular Models in a Hierarchical Modeling Topology

The Detailed Considerations: From Fuzzy Rule-Based Models to Granular Fuzzy Models

A Single-Level Knowledge Reconciliation: Mechanisms of Collaboration

Collaboration Scheme: Information Granules as Sources of Knowledge and a Development of Information Granules of a Higher Type

Structure-Free Granular Models

The Essence of Mappings between Input and Output Information Granules and the Underlying Processing

The Design of Information Granules in the Output Space and the Realization of the Aggregation Process

The Development of the Output Information Granules with the Use of the Principle of Justifiable Granularity

Interpretation of Granular Mappings

Illustrative Examples

Granular Time Series

Introductory Notes

Information Granules and Time Series

A Granular Framework of Interpretation of Time Series: A Layered Approach to the Interpretation of Time Series

A Classification Framework of Granular Time Series

Granular Classifiers

From Models to Granular Models

Knowledge Transfer in System Modeling

Fuzzy Logic Networks—Architectural Considerations

Granular Logic Descriptors

Granular Neural Networks

The Design of Granular Fuzzy Takagi–Sugeno Rule-Based Models: An Optimal Allocation of Information Granularity

Collaborative and Linguistic Models of Decision Making

Analytic Hierarchy Process (AHP) Method and Its Granular Generalization

Analytic Hierarchy Process Model—The Concept

Granular Reciprocal Matrices

A Quantification (Granulation) of Linguistic Terms as Their Operational Realization

Granular Logic Operators

Modes of Processing with Granular Characterization of Fuzzy Sets


Chapters include Conclusions and References.

About the Author

Witold Pedrycz, Ph.D., is Professor and Canada Research Chair (CRC) in Computational Intelligence 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, Warsaw, Poland and King Abdulaziz University, Saudi Arabia. In 2009, Dr. Pedrycz was elected a foreign member of the Polish Academy of Sciences. He is a Fellow of the Royal Society of Canada, the Institute of Electronic and Electrical Engineers (IEEE), International Fuzzy Systems Association (IFSA), International Society of Management Engineers, Engineers Canada, and The Engineering Institute of Canada. He is editor-in-chief of Information Sciences and editor-in-chief of IEEE Transactions on Systems, Man, and Cybernetics, Part A. He currently serves as an associate editor of IEEE Transactions on Fuzzy Systems and a number of other international journals. In 2007, he received the prestigious Norbert Wiener award from the IEEE Systems, Man, and Cybernetics Society. Dr. Pedrycz is a recipient of the IEEE Canada Computer Engineering Medal. In 2009, he received a Cajastur Prize for Soft Computing from the European Centre for Soft Computing for "pioneering and multifaceted contributions to granular computing." In 2013 he received a prestigious Killam Prize.

About the Series

Industrial Electronics

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Subject Categories

BISAC Subject Codes/Headings:
COMPUTERS / Software Development & Engineering / Systems Analysis & Design
TECHNOLOGY & ENGINEERING / Electronics / General