Granular, fuzzy, and soft computing [electronic resource] / Tsau-Young Lin, Churn-Jung Liau, Janusz Kacprzyk, editors.

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Granular, fuzzy, and soft computing [electronic resource] / Tsau-Young Lin, Churn-Jung Liau, Janusz Kacprzyk, editors.

9781071626283 (electronic bk.)
1071626280 (electronic bk.)
1071626272
9781071626276

New York, NY : Springer, 2023.

English

1 online resource (936 pages).

10.1007/978-1-0716-2628-3 doi

QA76.9.S63

006.3

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.

Discrete Interval Valued Type 2 Fuzzy Sets (DIVT2FS)
Includes index.

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
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

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Encyclopedia of complexity and systems science series.

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