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Hoboken : Wiley, [2016]

xiv, 247 stran ; ilustrace ; 25 cm

ISBN 978-1-119-19318-0 (vázáno)

Obsahuje bibliografii na stranách 235-242 a rejstřík

001450820

Preface xiii // Acknowledgments XV // About the Companion Website xvii // PART I FUNDAMENTALS OF FUZZY MODELING 1 // 1 What is Fuzzy Modeling 3 // 1.1 Indeterminacy in Human Life, 3 // 1.2 Fuzzy Modeling: With and Without Words, 6 // 2 Overview of Basic Notions 11 // 2.1 Relations, Functions, Ordered Sets, 11 // 2.1.1 Relations, 11 // 2.2 Fuzzy Sets and Fuzzy Relations, 14 // 2.2.1 The Concept of a Fuzzy Set, 14 // 2.2.2 Operations with Fuzzy Sets, 19 // 2.2.3 Fuzzy Numbers, 28 // 2.2.4 Fuzzy Partition and Fuzzy Covering, 31 // 2.2.5 Cartesian Product and Fuzzy Relations, 32 // 2.2.6 Fuzzy Equality and Extensional Fuzzy Sets, 37 // 2.3 Elements of Mathematical Fuzzy Logic, 41 // 2.3.1 Structure of Truth Degrees in Mathematical Fuzzy Logic, 41 // 2.3.2 Logical Inference, 43 // 2.3.3 Formal Systems of MFL, 45 // 2.3.4 The Concept of Fuzzy IF-THEN Rule, 46 // x // CONTENTS // 3 Fuzzy IF-THEN Rules in Approximation of Functions 49 // 3.1 Relational Interpretation of Fuzzy IF-THEN Rules, 49 // 3.1.1 Finite Functions and Their Description, 50 // 3.1.2 Relational Interpretation of Linguistic Descriptions, 53 // 3.1.3 Managing More Variables, 59 // 3.2 Approximation of Functions Using Fuzzy IF-THEN Rules, 60 // 3.2.1 Defuzzification, 60 // 3.2.2 Fuzzy Approximation, 63 // 3.2.3 Choosing between DNF and CNF, 69 // 3.3 Generalized Modus Ponens and Fuzzy Functions, 72 // 3.4 Takagi-Sugeno Rules, 74 // 3.4.1 Basic Concepts, 74 // 3.4.2 Fuzzy Approximation Using TS Rules, 75

3.4.3 Identification of TS Rules, 78 // 4 Fuzzy Transform 81 // 4.1 Fuzzy Partition, 81 // 4.2 The Concept of F-Transform, 84 // 4.2.1 Direct F-Transform, 84 // 4.2.2 Inverse F-Transform, 85 // 4.3 Discrete F-Transform, 88 // 4.4 F-Transform of Functions of Two Variables, 89 // 4.5 F-Transform, 91 // 4.6 Methodological Remarks to Applications of the F-Transform, 94 // 5 Fuzzy Natural Logic and Approximate Reasoning 97 // 5.1 Linguistic Semantics and Linguistic Variable, 97 // 5.1.1 Linguistic Variable, 98 // 5.1.2 Intension, Context, Extension, 98 // 5.1.3 Refined Definition of Linguistic Variable, 100 // 5.2 Theory of Evaluative Linguistic Expressions, 101 // 5.2.1 The Concept and Structure of Evaluative Expressions, 101 // 5.2.2 Evaluative Linguistic Predications, 105 // 5.2.3 Mathematical Model of the Semantics of Evaluative Linguistic Expressions, 106 // 5.3 Interpretation of Fuzzy/Linguistic IF-THEN Rules, 117 // 5.3.1 Linguistic Description, 117 // 5.3.2 Intension of Fuzzy/Linguistic IF-THEN Rules, 118 // 5.4 Approximate Reasoning with Linguistic Information, 119 // 5.4.1 Basic Principle of Approximate Reasoning, 119 // 5.4.2 Perception-Based Logical Deduction, 120 // 5.4.3 Formalization of the Perception-Based Logical Deduction, 124 // 5.4.4 Comparison of Two Interpretations of Fuzzy IF-THEN Rules, 128 // : j STENTS // xi // 6 Fuzzy Cluster Analysis 137 // 6.1 Basic Notions, 137 // 6.2 Fuzzy Clustering Algorithms, 139 // 6.3 The Algorithm of Fuzzy c-Means, 140 // 6.4 The

Gustafson-Kessel Algorithm, 142 // 6.5 Flow the Number of Clusters Can Be Determined, 144 // 6.6 Construction of Fuzzy Rules Based on Found Clusters, 144 // PART II SELECTED APPLICATIONS 149 // 7 Fuzzy/Linguistic Control and Decision-Making 151 // 7.1 The Principle of Fuzzy Control, 151 // 7.1.1 Control in a Closed Feedback Loop, 153 // 7.1.2 A General Scheme of Fuzzy Controller, 154 // 7.2 Fuzzy Controllers, 157 // 7.2.1 Variables, 157 // 7.2.2 Basic Types of Classical Controllers, 158 // 7.2.3 Basic Types of Fuzzy Controllers, 159 // 7.3 Design of Fuzzy/Linguistic Controller, 161 // 7.3.1 Determination of Variables and Linguistic Context, 161 // 7.3.2 Choosing Fuzzy Action Unit, 162 // 7.3.3 Formation of Knowledge Base, 163 // 7.3.4 Tuning Linguistic Description, 166 // 7.4 Learning, 171 // 7.4.1 Modification and Learning of Linguistic Context, 171 // 7.4.2 Learning Linguistic Description, 174 // 7.4.3 Practical Experiences with Control Using Linguistic Fuzzy Action Unit, 177 // 7.5 Decision-Making Using Linguistic Descriptions, 180 // 7.5.1 Introduction, 180 // 7.5.2 Hierarchy of Linguistic Descriptions in Decision-Making, 181 // 7.5.3 Demonstration of the Decision-Making Methodology Using Linguistic Descriptions, 182 // 8 F-Transform in Image Processing 189 // 8.1 Image and Its Basic Processing Using F-Transform, 189 // 8.2 F-Transform-Based Image Compression and Reconstruction, 190 // 8.2.1 Basic Principles of Image Compression, 190 // 8.2.2 Simple F-Transform Compression,

191 // 8.2.3 Advanced Image Compression, 191 // 8.3 F-Transform Edge Detector, 193 // 8.4 F-Transform-Based Image Fusion, 195 // 8.4.1 Basic Idea of Image Fusion, 195 // 8.4.2 Simple F-Transform-Based Fusion Algorithm, 197 // xii // CONTENTS // 8.4.3 Complete F-Transform-Based Fusion Algorithm, 199 // 8.4.4 Enhanced Simple Fusion Algorithm, 201 // 8.5 F-Transform-Based Corrupted Image Reconstruction, 203 // 8.5.1 The Reconstruction Problem, 203 // 8.5.2 F-Transform-Based Reconstruction, 204 // 8.5.3 Demonstration Examples, 206 // 9 Analysis and Forecasting of Time Series 209 // 9.1 Classical Versus Fuzzy Models of Time Series, 210 // 9.1.1 Definition of Time Series, 210 // 9.1.2 Classical Models of Time Series, 210 // 9.1.3 Fuzzy Models of Time Series, 211 // 9.2 Analysis of Time Series Using F-Transform, 212 // 9.2.1 Decomposition of Time Series, 212 // 9.2.2 Extraction of Trend-Cycle and Trend Using F-Transform, 214 // 9.3 Time Series Forecasting, 219 // 9.3.1 Decomposition of Time Domain, 219 // 9.3.2 Forecast of Trend-Cycle, 220 // 9.3.3 Forecast of Seasonal Component, 223 // 9.3.4 Forecast of the Whole Time Series, 225 // 9.4 Characterization of Time Series in Natural Language, 225 // 9.4.1 Sentences Characterizing Trend, 226 // 9.4.2 Automatic Generation of Sentences Characterizing Trend, 228 // 9.4.3 Mining Information from Time Series, 230 // References // Index 243