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Preface xiii <p>Contributors xvii</p> <p>1 Introduction 1</p> <p>1.1 Early History of Fuzzy Control 1</p> <p>1.2 What Is a Type-1 Fuzzy Set? 2</p> <p>1.3 What Is a Type-1 Fuzzy Logic Controller? 3</p> <p>1.4 What Is a Type-2 Fuzzy Set? 7</p> <p>1.5 What Is a Type-2 Fuzzy Logic Controller? 9</p> <p>1.6 Distinguishing an FLC from Other Nonlinear Controllers 10</p> <p>1.7 T2 FLCs versus T1 FLCs 11</p> <p>1.8 Real-World Applications of IT2 Mamdani FLCs 14</p> <p>1.8.1 Applications to Industrial Control 14</p> <p>1.8.2 Airplane Altitude Control 23</p> <p>1.8.3 Control of Mobile Robots 24</p> <p>1.8.4 Control of Ambient Intelligent Environments 27</p> <p>1.9 Book Rationale 29</p> <p>1.10 Software and How it Can Be Accessed 30</p> <p>1.11 Coverage of the Other Chapters 30</p> <p>2 Introduction to Type-2 Fuzzy Sets 32</p> <p>2.1 Introduction 32</p> <p>2.2 Brief Review of Type-1 Fuzzy Sets 32</p> <p>2.2.1 Some Definitions 32</p> <p>2.2.2 Set-Theoretic Operations 35</p> <p>2.2.3 Alpha Cuts 36</p> <p>2.2.4 Compositions of T1 FSs 39</p> <p>2.2.5 Rules and Their MFs 40</p> <p>2.3 Interval Type-2 Fuzzy Sets 42</p> <p>2.3.1 Introduction 42</p> <p>2.3.2 Definitions 43</p> <p>2.3.3 Set-Theoretic Operations 51</p> <p>2.3.4 Centroid of an IT2 FS 54</p> <p>2.3.5 Properties of cl(k) and cr(k) 58</p> <p>2.3.6 KM Algorithms as Well as Some Others 59</p> <p>2.4 General Type-2 Fuzzy Sets 68</p> <p>2.4.1 -Plane/zSlice Representation 68</p> <p>2.4.2 Set-Theoretic Operations 72</p> <p>2.4.3 Centroid of a GT2 FS 73</p> <p>2.5 Wrapup 77</p> <p>2.6 Moving On 79</p> <p>3 Interval Type-2 Fuzzy Logic Controllers 80</p> <p>3.1 Introduction 80</p> <p>3.2 Type-1 Fuzzy Logic Controllers 80</p> <p>3.2.1 Introduction 80</p> <p>3.2.2 T1 Mamdani FLCs 81</p> <p>3.2.3 T1 TSK FLCs 85</p> <p>3.2.4 Design of T1 FLCs 86</p> <p>3.3 Interval Type-2 Fuzzy Logic Controllers 86</p> <p>3.3.1 Introduction 86</p> <p>3.3.2 IT2 Mamdani FLCs 87</p> <p>3.3.3 IT2 TSK FLCs 103</p> <p>3.3.4 Design of T2 FLCs 105</p> <p>3.4 Wu–Mendel Uncertainty Bounds 105</p> <p>3.5 Control Analyses of IT2 FLCs 111</p> <p>3.6 Determining the FOU Parameters of IT2 FLCs 114</p> <p>3.6.1 Blurring T1 MFs 114</p> <p>3.6.2 Optimizing FOU Parameters 114</p> <p>3.7 Moving On 122</p> <p>Appendix 3A. Proof of Theorem 3.4 123</p> <p>3A.1 Inner-Bound Set [ul(), ur()] 123</p> <p>3A.2 Outer-Bound Set [ul(), ur()] 124</p> <p>4 Analytical Structure of Various Interval Type-2 Fuzzy PI and PD Controllers 131</p> <p>4.1 Introduction 131</p> <p>4.2 PID, PI, and PD Controllers and Their Relationships 134</p> <p>4.2.1 Two Forms of PID Controller—Position Form and Incremental Form 134</p> <p>4.2.2 PI and PD Controllers and Their Relationship 135</p> <p>4.3 Components of the Interval T2 Fuzzy PI and PD Controllers 136</p> <p>4.4 Mamdani Fuzzy PI and PD Controllers—Configuration 1 140</p> <p>4.4.1 Fuzzy PI Controller Configuration 140</p> <p>4.4.2 Method for Deriving the Analytical Structure 144</p> <p>4.5 Mamdani Fuzzy PI and PD Controllers—Configuration 2 154</p> <p>4.6 Mamdani Fuzzy PI and PD Controllers—Configuration 3 162</p> <p>4.6.1 Fuzzy PI Controller Configuration 162</p> <p>4.6.2 Method for Deriving the Analytical Structure 165</p> <p>4.7 Mamdani Fuzzy PI and PD Controllers—Configuration 4 169</p> <p>4.7.1 Fuzzy PI Controller Configuration 169</p> <p>4.7.2 Method for Deriving the Analytical Structure 171</p> <p>4.8 TSK Fuzzy PI and PD Controllers—Configuration 5 181</p> <p>4.8.1 Fuzzy PI Controller Configuration 181</p> <p>4.8.2 Deriving the Analytical Structure 184</p> <p>4.9 Analyzing the Derived Analytical Structures 185</p> <p>4.9.1 Structural Connection with the Corresponding T1 Fuzzy PI Controller 186</p> <p>4.9.2 Characteristics of the Variable Gains of the T2 Fuzzy PI Controller 190</p> <p>4.10 Design Guidelines for the T2 Fuzzy PI and PD Controllers 194</p> <p>4.10.1 Determination of 1 and 2 Values 196</p> <p>4.10.2 Determination of the Remaining Nine Parameter Values 197</p> <p>4.11 Summary 198</p> <p>Appendix 4A 200</p> <p>5 Analysis of Simplified Interval Type-2 Fuzzy PI and PD Controllers 205</p> <p>5.1 Introduction 205</p> <p>5.2 Simplified Type-2 FLCs: Design, Computation, and Performance 206</p> <p>5.2.1 Structure of a Simplified IT2 FLC 207</p> <p>5.2.2 Output Computation 208</p> <p>5.2.3 Computational Cost 209</p> <p>5.2.4 Genetic Tuning of FLC 210</p> <p>5.2.5 Performance 211</p> <p>5.2.6 Discussions 216</p> <p>5.3 Analytical Structure of Interval T2 Fuzzy PD and PI Controller 221</p> <p>5.3.1 Configuration of Interval T2 Fuzzy PD and PI Controller 221</p> <p>5.3.2 Analysis of the Karnik–Mendel Type-Reduced IT2 Fuzzy PD Controller 227</p> <p>6.7 Robust Control Design 277</p> <p>6.7.1 System Description 277</p> <p>6.7.2 Disturbance Rejection Problem and Solution 280</p> <p>6.7.3 Robust Control Example 284</p> <p>6.8 Summary 285</p> <p>Appendix 285</p> <p>7 Looking into the Future 290</p> <p>7.1 Introduction 290</p> <p>7.2 William Melek and Hao Ying Look into the Future 290</p> <p>7.3 Hani Hagras Looks into the Future 293</p> <p>7.3.1 Nonsingleton IT2 FL Control 293</p> <p>7.3.2 zSlices-Based Singleton General T2 FL Control 299</p> <p>7.4 Woei Wan Tan Looks into the Future 306</p> <p>7.5 Jerry Mendel Looks into The Future 307</p> <p>7.5.1 IT2 FLC 307</p> <p>7.5.2 GT2 FLC 309</p> <p>Appendix A T2 FLC Software: From Type-1 to zSlices-Based General Type-2 FLCs 315</p> <p>A.1 Introduction 315</p> <p>A.2 FLC for Right-Edge Following 315</p> <p>A.3 Type-1 FLC Software 316</p> <p>A.3.1 Define and Set Up T1 FLC Inputs 316</p> <p>A.3.2 Define T1 FSs That Quantify Each Variable 316</p> <p>A.3.3 Define Logical Antecedents and Consequents for the FL Rules 318</p> <p>A.3.4 Define Rule Base of T1 FLC 318</p> <p>A.4 Interval T2 FLC Software 321</p> <p>A.4.1 Define and Set Up FLC Inputs 323</p> <p>A.4.2 Define IT2 FSs That Quantify Each Variable 323</p> <p>A.4.3 Define Logical Antecedents and Consequents for the FL Rules 323</p> <p>A.4.4 Define Rule Base of the IT2 FLC 323</p> <p>A.5 zSlices-Based General Type-2 FLC Software 327</p> <p>A.5.1 Define and Set Up FLC Inputs 327</p> <p>A.5.2 Define zSlices-Based GT2 FSs That Quantify Each Variable 327</p> <p>A.5.3 Define Logical Antecedents and Consequents for the FL Rules 335</p> <p>A.5.4 Define Rule Base of the GT2 FLC 335</p> <p>References 338</p> <p>Index 347</p>

<p><b>JERRY M. MENDEL</b> is Professor in the Ming Hsieh Department of Electrical Engineering at the University of Southern California, Life Fellow of the IEEE, and a Distinguished Member of the IEEE Control Systems Society.</p> <p><b>HANI HAGRAS</b> is Professor and Director of the Computational Intelligence Centre in the School of Computer Science and Electronic Engineering at the University of Essex, UK, and is a Fellow of the IEEE.</p> <p><b>WOEI-WAN TAN</b> is Associate Professor in the Department of Electrical Engineering at the National University of Singapore.</p> <p><b>WILLIAM W. MELEK</b> is Associate Professor in the Department of Mechanical and Mechatronics Engineering at the University of Waterloo.</p> <p><b>HAO YING</b> is Professor in the Department of Electrical and Computer Engineering at Wayne State University and a Fellow of the IEEE.</p>

<p><b>An introductory book that provides theoretical, practical, and application coverage of the emerging field of type-2 fuzzy logic control</b></p> <p>Until recently, little was known about type-2 fuzzy controllers due to the lack of basic calculation methods available for type-2 fuzzy sets and logic—and many different aspects of type-2 fuzzy control still needed to be investigated in order to advance this new and powerful technology. This self-contained reference covers everything readers need to know about the growing field.</p> <p>Written with an educational focus in mind, <i>Introduction to Type-2 Fuzzy Logic Control: Theory and Applications</i> uses a coherent structure and uniform mathematical notations to link chapters that are closely related, reflecting the book’s central themes: analysis and design of type-2 fuzzy control systems. The book includes worked examples, experiment and simulation results, and comprehensive reference materials. The book also offers downloadable computer programs from an associated website.</p> <p>Presented by world-class leaders in type-2 fuzzy logic control, <i>Introduction to Type-2 Fuzzy Logic Control</i>:</p> <ul> <li>Is useful for any technical person interested in learning type-2 fuzzy control theory and its applications</li> <li>Offers experiment and simulation results via downloadable computer programs</li> <li>Features type-2 fuzzy logic background chapters to make the book self-contained</li> <li>Provides an extensive literature survey on both fuzzy logic and related type-2 fuzzy control</li> </ul> <p><i>Introduction to Type-2 Fuzzy Logic Control</i> is an easy-to-read reference book suitable for engineers, researchers, and graduate students who want to gain deep insight into type-2 fuzzy logic control.</p>

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