Handbook of Granular Computing
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More About This Title Handbook of Granular Computing


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. 


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.





Part One Fundamentals and Methodology of Granular Computing Based on Interval Analysis, Fuzzy Sets and Rough Sets.

1 Interval Computation as an Important Part of Granular Computing: An Introduction (Vladik Kreinovich).

2 Stochastic Arithmetic as a Model of Granular Computing (René Alt and Jean Vignes).

3 Fundamentals of Interval Analysis and Linkages to Fuzzy Set Theory (Weldon A. Lodwick).

4 Interval Methods for Non-Linear Equation Solving Applications (Courtney Ryan Gwaltney, Youdong Lin, Luke David Simoni, and Mark Allen Stadtherr).

5 Fuzzy Sets as a User-Centric Processing Framework of Granular Computing (Witold Pedrycz).

6 Measurement and Elicitation of Membership Functions (Taner Bilgiç andÄ°.Burhan TürkÅ?en).

7 Fuzzy Clustering as a Data-Driven Development Environment for Information Granules (Paulo Fazendeiro and José Valente de Oliveira).

8 Encoding and Decoding of Fuzzy Granules (Shounak Roychowdhury).

9 Systems of Information Granules (Frank Hoeppner and Frank Klawann).

10 Logical Connectives for Granular Computing (Erich Peter Klement, Radko Mesiar, Andrea Mesiarová-Zemánková and Susanne Saminger-Platz).

11 Calculi of Information Granules. Fuzzy Relational Equations (Siegfried Gottwald).

12 Fuzzy Numbers and Fuzzy Arithmetic (Luciano Stefanini, Laerte Sorini, and Maria Letizia Guerra).

13 Rough-Granular Computing (Andrzej Skowron and James F. Peters).

14 Wisdom Granular Computing (Andrzej Jankowski and Andrzej Skowron).

15 Granular Computing for Reasoning about Ordered Data: The Dominance-BasedRough Set Approach (Salvatore Greco, Benedetto Matarazzo, and Roman SlowiÅ?ski).

16 A Unified Approach to Granulation of Knowledge and Granular ComputingBased on Rough Mereology: A Survey (Lech Polkowski).

17 A Unified Framework of Granular Computing (Yiyu Yao).

18 Quotient Spaces and Granular Computing (Ling Zhang and Bo Zhang).

19 Rough Sets and Granular Computing: Toward Rough-Granular Computing (Andrzej Skowron and Jaroslaw Stepaniuk).

20 Construction of Rough Information Granules (Anna GomoliÅ?ska).

21 Spatiotemporal Reasoning in Rough Sets and Granular Computing(Piotr Synak).

Part Two Hybrid Methods and Models of Granular Computing.

22 A Survey of Interval-Valued Fuzzy Sets (Humberto Bustince, Javier Montero, Miguel Pagola, Edurne Barrenechea, and Daniel Gomez).

23 Measurement Theory and Uncertainty in Measurements: Application of Interval Analysis and Fuzzy Sets Methods (Leon Reznik).

24 Fuzzy Rough Sets: From Theory into Practice (Chris Cornelis, Martine De Cock, and Anna Maria Radzikowska).

25 On Type 2 Fuzzy Sets as Granular Models for Words (Jerry M. Mendel).

26 Design of Intelligent Systems with Interval Type-2 Fuzzy Logic(Oscar Castillo and Patricia Melin).

27 Theoretical Aspects of Shadowed Sets (Gianpiero Cattaneo and Davide Ciucci).

28 Fuzzy Representations of Spatial Relations for Spatial Reasoning(Isabelle Bloch).

29 Roughâ??Neural Methodologies in Granular Computing (Sushmita Mitra and Mohua Banerjee).

30 Approximation and Perception in Ethology-Based Reinforcement Learning (James F. Peters).

31 Fuzzy Linear Programming (Jaroslav Ramík).

32 A Fuzzy Regression Approach to Acquisition of Linguistic Rules(Junzo Watada and Witold Pedrycz).

33 Fuzzy Associative Memories and Their Relationship to Mathematical Morphology (Peter Sussner and Marcos Eduardo Valle).

34 Fuzzy Cognitive Maps (E.I. Papageorgiou and C.D. Stylios).

Part Three Applications and Case Studies.

35 Rough Sets and Granular Computing in Behavioral Pattern Identification and Planning (Jan G. Bazan).

36 Rough Sets and Granular Computing in Hierarchical Learning (Sinh Hoa Nguyen and Hung Son Nguyen).

37 Outlier and Exception Analysis in Rough Sets and Granular Computing (Tuan Trung Nyuyen).

38 Information Access and Retrieval (Gloria Bordogna, Donald H. Kraft, and Gabriella Pasi).

39 Granular Computing in Medical Informatics (Giovanni Bortolan).

40 Eigen Fuzzy Sets and Image Information Retrieval (Ferdinando Di Martino, Salvatore Sessa, and Hajime Nobuhara).

41 Rough Sets and Granular Computing in Dealing with Missing Attribute Values (Jerzy W. Grzymala-Busse).

42 Granular Computing in Machine Learning and Data Mining (Eyke Huellermeier).

43 On Group Decision Making, Consensus Reaching, Voting, and Voting Paradoxes under Fuzzy Preferences and a Fuzzy Majority: A Survey and a Granulation Perspective (Janusz Kacprzyk, Slawomir. Zadrożny, Mario Fedrizzi and Hannu Nurmi).

44 FuzzJADE: A Framework for Agent-Based FLCs (Vincenzo Loia and Mario Veniero).

45 Granular Models for Time-Series Forecasting (Marina Hirota Magalhães, Rosangela Ballini, and Fernando Gomide).

46 Rough Clustering (Pawan Lingras, S. Asharaf, and Cory Butz).

47 Rough Document Clustering and The Internet (Hung Son Nguyen and Tu Bao Ho).

48 Rough and Granular Case-Based Reasoning (Simon C.K. Shiu, Sankar K. Pal, and Yan Li).

49 Granulation in Analogy-Based Classification (Arkadiusz Wojna).

50 Approximation Spaces in Conflict Analysis: A Rough Set Framework(Sheela Ramanna).

51 Intervals in Finance and Economics: Bridge between Words and Numbers, Language of Strategy (Manuel Tarrazo).

52 Granular Computing Methods in Bioinformatics (JulioJ. Valdés).