Insight into Fuzzy Modeling
Providesa unique and methodologically consistent treatment of various areas of fuzzy modeling and includes the results of mathematical fuzzy logic and linguistics This book is the result of almost thirty years of research on fuzzy modeling. It provides a unique view of both the theory and various ty...
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| Médium: | E-kniha |
| Jazyk: | angličtina |
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Newark
Wiley
2016
John Wiley & Sons, Incorporated Wiley-Blackwell |
| Vydání: | 1 |
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| ISBN: | 1119193206, 9781119193203, 1119193184, 9781119193180 |
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| Abstract | Providesa unique and methodologically consistent treatment of various areas of fuzzy modeling and includes the results of mathematical fuzzy logic and linguistics
This book is the result of almost thirty years of research on fuzzy modeling. It provides a unique view of both the theory and various types of applications. The book is divided into two parts. The first part contains an extensive presentation of the theory of fuzzy modeling. The second part presents selected applications in three important areas: control and decision-making, image processing, and time series analysis and forecasting. The authors address the consistent and appropriate treatment of the notions of fuzzy sets and fuzzy logic and their applications. They provide two complementary views of the methodology, which is based on fuzzy IF-THEN rules. The first, more traditional method involves fuzzy approximation and the theory of fuzzy relations. The second method is based on a combination of formal fuzzy logic and linguistics. A very important topic covered for the first time in book form is the fuzzy transform (F-transform). Applications of this theory are described in separate chapters and include image processing and time series analysis and forecasting. All of the mentioned components make this book of interest to students and researchers of fuzzy modeling as well as to practitioners in industry.
Features:
* Provides a foundation of fuzzy modeling and proposes a thorough description of fuzzy modeling methodology
* Emphasizes fuzzy modeling based on results in linguistics and formal logic
* Includes chapters on natural language and approximate reasoning, fuzzy control and fuzzy decision-making, and image processing using the F-transform
* Discusses fuzzy IF-THEN rules for approximating functions, fuzzy cluster analysis, and time series forecasting
Insight into Fuzzy Modeling is a reference for researchers in the fields of soft computing and fuzzy logic as well as undergraduate, master and Ph.D. students.
Vilém Novák, D.Sc. is Full Professor and Director of the Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, Czech Republic.
Irina Perfilieva, Ph.D. is Full Professor, Senior Scientist, and Head of the Department of Theoretical Research at the Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, Czech Republic.
Antonín Dvorák, Ph.D. is Associate Professor, and Senior Scientist at the Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, Czech Republic. |
|---|---|
| AbstractList | Provides a unique and methodologically consistent treatment of various areas of fuzzy modeling and includes the results of mathematical fuzzy logic and linguistics This book is the result of almost thirty years of research on fuzzy modeling. It provides a unique view of both the theory and various types of applications. The book is divided into two parts. The first part contains an extensive presentation of the theory of fuzzy modeling. The second part presents selected applications in three important areas: control and decision-making, image processing, and time series analysis and forecasting. The authors address the consistent and appropriate treatment of the notions of fuzzy sets and fuzzy logic and their applications. They provide two complementary views of the methodology, which is based on fuzzy IF-THEN rules. The first, more traditional method involves fuzzy approximation and the theory of fuzzy relations. The second method is based on a combination of formal fuzzy logic and linguistics. A very important topic covered for the first time in book form is the fuzzy transform (F-transform). Applications of this theory are described in separate chapters and include image processing and time series analysis and forecasting. All of the mentioned components make this book of interest to students and researchers of fuzzy modeling as well as to practitioners in industry. Features: Provides a foundation of fuzzy modeling and proposes a thorough description of fuzzy modeling methodology Emphasizes fuzzy modeling based on results in linguistics and formal logic Includes chapters on natural language and approximate reasoning, fuzzy control and fuzzy decision-making, and image processing using the F-transform Discusses fuzzy IF-THEN rules for approximating functions, fuzzy cluster analysis, and time series forecasting Insight into Fuzzy Modeling is a reference for researchers in the fields of soft computing and fuzzy logic as well as undergraduate, master and Ph.D. students. Vilém Novák, D.Sc. is Full Professor and Director of the Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, Czech Republic. Irina Perfilieva, Ph.D. is Full Professor, Senior Scientist, and Head of the Department of Theoretical Research at the Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, Czech Republic. Antonín Dvorák, Ph.D. is Associate Professor, and Senior Scientist at the Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, Czech Republic. Providesa unique and methodologically consistent treatment of various areas of fuzzy modeling and includes the results of mathematical fuzzy logic and linguistics This book is the result of almost thirty years of research on fuzzy modeling. It provides a unique view of both the theory and various types of applications. The book is divided into two parts. The first part contains an extensive presentation of the theory of fuzzy modeling. The second part presents selected applications in three important areas: control and decision-making, image processing, and time series analysis and forecasting. The authors address the consistent and appropriate treatment of the notions of fuzzy sets and fuzzy logic and their applications. They provide two complementary views of the methodology, which is based on fuzzy IF-THEN rules. The first, more traditional method involves fuzzy approximation and the theory of fuzzy relations. The second method is based on a combination of formal fuzzy logic and linguistics. A very important topic covered for the first time in book form is the fuzzy transform (F-transform). Applications of this theory are described in separate chapters and include image processing and time series analysis and forecasting. All of the mentioned components make this book of interest to students and researchers of fuzzy modeling as well as to practitioners in industry. Features: * Provides a foundation of fuzzy modeling and proposes a thorough description of fuzzy modeling methodology * Emphasizes fuzzy modeling based on results in linguistics and formal logic * Includes chapters on natural language and approximate reasoning, fuzzy control and fuzzy decision-making, and image processing using the F-transform * Discusses fuzzy IF-THEN rules for approximating functions, fuzzy cluster analysis, and time series forecasting Insight into Fuzzy Modeling is a reference for researchers in the fields of soft computing and fuzzy logic as well as undergraduate, master and Ph.D. students. Vilém Novák, D.Sc. is Full Professor and Director of the Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, Czech Republic. Irina Perfilieva, Ph.D. is Full Professor, Senior Scientist, and Head of the Department of Theoretical Research at the Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, Czech Republic. Antonín Dvorák, Ph.D. is Associate Professor, and Senior Scientist at the Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, Czech Republic. |
| Author | Vilém Novák, Irina Perfilieva, Antonín Dvorák |
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| Snippet | Providesa unique and methodologically consistent treatment of various areas of fuzzy modeling and includes the results of mathematical fuzzy logic and... Provides a unique and methodologically consistent treatment of various areas of fuzzy modeling and includes the results of mathematical fuzzy logic and... |
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| SubjectTerms | Fuzzy mathematics Fuzzy systems Mathematical models Simulation methods |
| TableOfContents | 8.1 IMAGE AND ITS BASIC PROCESSING USING F-TRANSFORM -- 8.2 F-TRANSFORM-BASED IMAGE COMPRESSION AND RECONSTRUCTION -- 8.3 F1-TRANSFORM EDGE DETECTOR -- 8.4 F-TRANSFORM-BASED IMAGE FUSION -- 8.5 F-TRANSFORM-BASED CORRUPTED IMAGE RECONSTRUCTION -- Chapter 9: Analysis and Forecasting of Time Series -- 9.1 CLASSICAL VERSUS FUZZY MODELS OF TIME SERIES -- 9.2 ANALYSIS OF TIME SERIES USING F-TRANSFORM -- 9.3 TIME SERIES FORECASTING -- 9.4 CHARACTERIZATION OF TIME SERIES IN NATURAL LANGUAGE -- References -- Index -- End User License Agreement Intro -- Title Page -- Copyright -- Table of Contents -- Dedication -- Preface -- Acknowledgments -- About the Companion Website -- PART I: FUNDAMENTALS OF FUZZY MODELING -- Chapter 1: What is Fuzzy Modeling -- 1.1 INDETERMINACY IN HUMAN LIFE -- 1.2 FUZZY MODELING: WITH AND WITHOUT WORDS -- Chapter 2: Overview of Basic Notions -- 2.1 RELATIONS, FUNCTIONS, ORDERED SETS -- 2.2 FUZZY SETS AND FUZZY RELATIONS -- 2.3 ELEMENTS OF MATHEMATICAL FUZZY LOGIC -- Chapter 3: Fuzzy If-Then Rules in Approximation Of Functions -- 3.1 RELATIONAL INTERPRETATION OF FUZZY IF-THEN RULES -- 3.2 APPROXIMATION OF FUNCTIONS USING FUZZY IF-THEN RULES -- 3.3 GENERALIZED MODUS PONENS AND FUZZY FUNCTIONS -- 3.4 TAKAGI-SUGENO RULES -- Chapter 4: Fuzzy Transform -- 4.1 FUZZY PARTITION -- 4.2 THE CONCEPT OF F-TRANSFORM -- 4.3 DISCRETE F-TRANSFORM -- 4.4 F-TRANSFORM OF FUNCTIONS OF TWO VARIABLES -- 4.5 F1-TRANSFORM -- 4.6 METHODOLOGICAL REMARKS TO APPLICATIONS OF THE F-TRANSFORM -- Chapter 5: Fuzzy Natural Logic and Approximate Reasoning -- 5.1 LINGUISTIC SEMANTICS AND LINGUISTIC VARIABLE -- 5.2 THEORY OF EVALUATIVE LINGUISTIC EXPRESSIONS -- 5.3 INTERPRETATION OF FUZZY/LINGUISTIC IF-THEN RULES -- 5.4 APPROXIMATE REASONING WITH LINGUISTIC INFORMATION -- Chapter 6: Fuzzy Cluster Analysis -- 6.1 BASIC NOTIONS -- 6.2 FUZZY CLUSTERING ALGORITHMS -- 6.3 THE ALGORITHM OF FUZZY c-MEANS -- 6.4 THE GUSTAFSON-KESSEL ALGORITHM -- 6.5 HOW THE NUMBER OF CLUSTERS CAN BE DETERMINED -- 6.6 CONSTRUCTION OF FUZZY RULES BASED ON FOUND CLUSTERS -- PART II: SELECTED APPLICATIONS -- Chapter 7: Fuzzy/Linguistic Control and Decision-Making -- 7.1 THE PRINCIPLE OF FUZZY CONTROL -- 7.2 FUZZY CONTROLLERS -- 7.3 DESIGN OF FUZZY/LINGUISTIC CONTROLLER -- 7.4 LEARNING -- 7.5 DECISION-MAKING USING LINGUISTIC DESCRIPTIONS -- Chapter 8: F-Transform in Image Processing |
| Title | Insight into Fuzzy Modeling |
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