| Description |
1 online resource (936 p.) |
| Series |
Encyclopedia of Complexity and Systems Science Series |
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Encyclopedia of complexity and systems science series.
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| Contents |
Intro -- Series Preface -- Volume Preface -- Soft and Nature-Inspired Computing -- Mathematical Fuzzy Sets and Rough Sets -- (Generalized) Topological Computing -- Granular Computing (GRC) -- Soft and Various Forms of Intelligent Computing -- Contents -- About the Editor-in-Chief -- About the Volume Editors -- Contributors -- Cooperative Multi-hierarchical Query Answering Systems -- Glossary -- Definition of the Subject -- Introduction -- Multi-hierarchical Decision System -- Cooperative Query Answering -- Future Directions -- Bibliography -- Dependency and Granularity in Data-Mining |
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Definition of the Subject -- Introduction -- Contingency Table from Rough Sets -- Notations -- Contingency Table (m x n) -- Rank of Contingency Table (2 x 2) -- Preliminaries -- Independence When the Table Is 2 x 2 -- Rank of Contingency Table (m x n) -- Rank and Degree of Dependence -- Submatrix and Subdeterminant -- Rank and Subdeterminant -- Rank and Submatrix -- Determinantal Divisors -- Divisors and Degree of Dependence -- Subdeterminants and Degree of Dependence -- Elementary Divisors and Elementary Transformation -- Degree of Granularity and Dependence -- Conclusion -- Acknowledgments |
| Summary |
The first edition of the Encyclopedia of Complexity and Systems Science (ECSS, 2009) presented a comprehensive overview of granular computing (GrC) broadly divided into several categories: Granular computing from rough set theory, Granular Computing in Database Theory, Granular Computing in Social Networks, Granular Computing and Fuzzy Set Theory, Grid/Cloud Computing, as well as general issues in granular computing. In 2011, the formal theory of GrC was established, providing an adequate infrastructure to support revolutionary new approaches to computer/data science, including the challenges presented by so-called big data. For this volume of ECSS, Second Edition, many entries have been updated to capture these new developments, together with new chapters on such topics as data clustering, outliers in data mining, qualitative fuzzy sets, and information flow analysis for security applications. Granulations can be seen as a natural and ancient methodology deeply rooted in the human mind. Many daily "things" are routinely granulated into sub "things": The topography of earth is granulated into hills, plateaus, etc., space and time are granulated into infinitesimal granules, and a circle is granulated into polygons of infinitesimal sides. Such granules led to the invention of calculus, topology and non-standard analysis. Formalization of general granulation was difficult but, as shown in this volume, great progress has been made in combing discrete and continuous mathematics under one roof for a broad range of applications in data science |
| Bibliography |
Bibliography -- Fuzzy Logic -- Glossary -- Definition of the Subject -- Introduction -- Conceptual Structure of Fuzzy Logic -- The Basics of Fuzzy Set Theory -- The Concept of Granulation -- The Concepts of Precisiation and Cointensive Precisiation -- The Concept of Cointension -- The Concept of a Generalized Constraint -- Constrained Variable -- Modalities of Generalized Constraints -- Possibilistic Constraint -- Probabilistic Constraint -- Veristic Constraint (Zadeh 1999, 2005a) -- Fuzzy Graph Constraint -- Usuality Constraint (Zadeh 1999, 2002) -- Primary Constraints -- Standard Constraints |
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Bibliography -- Primary Literature -- Books and Reviews -- Fuzzy System Models Evolution from Fuzzy Rulebases to Fuzzy Functions -- Glossary -- Definition of the Subject -- Introduction -- Type 1 Fuzzy System Models of the Past -- Type 1 Fuzzy Rulebases -- Type 1 ̀̀Special Fuzzy Functions ́́of the Recent Past -- Special Fuzzy Functions with LSE (SFF-LSE) Method -- Support Vector Machines for Regression -- Special Fuzzy Functions with SVM (FF-SVM) Method -- Future of Fuzzy System Models -- Basic Definitions -- General Structure of Type 2 Fuzzy System Models |
| Notes |
Discrete Interval Valued Type 2 Fuzzy Sets (DIVT2FS) |
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Includes index |
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Print version record |
| Subject |
Granular computing.
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Granular computing
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| Form |
Electronic book
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| Author |
Lin, Tsau Y., 1937-
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Liau, Churn-Jung
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Kacprzyk, Janusz.
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| ISBN |
9781071626283 |
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1071626280 |
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