{"product_id":"introduction-to-type2-fuzzy-logic-control-9781118278390","title":"Introduction To Type2 Fuzzy Logic Control","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eAn introductory book that provides theoretical, practical, and application coverage of the emerging field of type-2 fuzzy logic control\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eUntil recently, little was known about type-2 fuzzy controllers due to the lack of basic calculation methods available for type-2 fuzzy sets and logicand 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.\u003c\/p\u003e \u003cp\u003eWritten with an educational focus in mind, \u003ci\u003eIntroduction to Type-2 Fuzzy Logic Control: Theory and Applications\u003c\/i\u003e 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 com\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface xiii  \u003c\/p\u003e\u003cp\u003eContributors xvii\u003c\/p\u003e \u003cp\u003e1 Introduction 1\u003c\/p\u003e \u003cp\u003e1.1 Early History of Fuzzy Control 1\u003c\/p\u003e \u003cp\u003e1.2 What Is a Type-1 Fuzzy Set? 2\u003c\/p\u003e \u003cp\u003e1.3 What Is a Type-1 Fuzzy Logic Controller? 3\u003c\/p\u003e \u003cp\u003e1.4 What Is a Type-2 Fuzzy Set? 7\u003c\/p\u003e \u003cp\u003e1.5 What Is a Type-2 Fuzzy Logic Controller? 9\u003c\/p\u003e \u003cp\u003e1.6 Distinguishing an FLC from Other Nonlinear Controllers 10\u003c\/p\u003e \u003cp\u003e1.7 T2 FLCs versus T1 FLCs 11\u003c\/p\u003e \u003cp\u003e1.8 Real-World Applications of IT2 Mamdani FLCs 14\u003c\/p\u003e \u003cp\u003e1.8.1 Applications to Industrial Control 14\u003c\/p\u003e \u003cp\u003e1.8.2 Airplane Altitude Control 23\u003c\/p\u003e \u003cp\u003e1.8.3 Control of Mobile Robots 24\u003c\/p\u003e \u003cp\u003e1.8.4 Control of Ambient Intelligent Environments 27\u003c\/p\u003e \u003cp\u003e1.9 Book Rationale 29\u003c\/p\u003e \u003cp\u003e1.10 Software and How it Can Be Accessed 30\u003c\/p\u003e \u003cp\u003e1.11 Coverage of the Other Chapters 30\u003c\/p\u003e \u003cp\u003e2 Introduction to Type-2 Fuzzy Sets 32\u003c\/p\u003e \u003cp\u003e2.1 Introduction 32\u003c\/p\u003e \u003cp\u003e2.2 Brief Review of Type-1 Fuzzy Sets 32\u003c\/p\u003e \u003cp\u003e2.2.1 Some Definitions 32\u003c\/p\u003e \u003cp\u003e2.2.2 Set-Theoretic Operations 35\u003c\/p\u003e \u003cp\u003e2.2.3 Alpha Cuts 36\u003c\/p\u003e \u003cp\u003e2.2.4 Compositions of T1 FSs 39\u003c\/p\u003e \u003cp\u003e2.2.5 Rules and Their MFs 40\u003c\/p\u003e \u003cp\u003e2.3 Interval Type-2 Fuzzy Sets 42\u003c\/p\u003e \u003cp\u003e2.3.1 Introduction 42\u003c\/p\u003e \u003cp\u003e2.3.2 Definitions 43\u003c\/p\u003e \u003cp\u003e2.3.3 Set-Theoretic Operations 51\u003c\/p\u003e \u003cp\u003e2.3.4 Centroid of an IT2 FS 54\u003c\/p\u003e \u003cp\u003e2.3.5 Properties of cl(k) and cr(k) 58\u003c\/p\u003e \u003cp\u003e2.3.6 KM Algorithms as Well as Some Others 59\u003c\/p\u003e \u003cp\u003e2.4 General Type-2 Fuzzy Sets 68\u003c\/p\u003e \u003cp\u003e2.4.1 -Plane\/zSlice Representation 68\u003c\/p\u003e \u003cp\u003e2.4.2 Set-Theoretic Operations 72\u003c\/p\u003e \u003cp\u003e2.4.3 Centroid of a GT2 FS 73\u003c\/p\u003e \u003cp\u003e2.5 Wrapup 77\u003c\/p\u003e \u003cp\u003e2.6 Moving On 79\u003c\/p\u003e \u003cp\u003e3 Interval Type-2 Fuzzy Logic Controllers 80\u003c\/p\u003e \u003cp\u003e3.1 Introduction 80\u003c\/p\u003e \u003cp\u003e3.2 Type-1 Fuzzy Logic Controllers 80\u003c\/p\u003e \u003cp\u003e3.2.1 Introduction 80\u003c\/p\u003e \u003cp\u003e3.2.2 T1 Mamdani FLCs 81\u003c\/p\u003e \u003cp\u003e3.2.3 T1 TSK FLCs 85\u003c\/p\u003e \u003cp\u003e3.2.4 Design of T1 FLCs 86\u003c\/p\u003e \u003cp\u003e3.3 Interval Type-2 Fuzzy Logic Controllers 86\u003c\/p\u003e \u003cp\u003e3.3.1 Introduction 86\u003c\/p\u003e \u003cp\u003e3.3.2 IT2 Mamdani FLCs 87\u003c\/p\u003e \u003cp\u003e3.3.3 IT2 TSK FLCs 103\u003c\/p\u003e \u003cp\u003e3.3.4 Design of T2 FLCs 105\u003c\/p\u003e \u003cp\u003e3.4 Wu–Mendel Uncertainty Bounds 105\u003c\/p\u003e \u003cp\u003e3.5 Control Analyses of IT2 FLCs 111\u003c\/p\u003e \u003cp\u003e3.6 Determining the FOU Parameters of IT2 FLCs 114\u003c\/p\u003e \u003cp\u003e3.6.1 Blurring T1 MFs 114\u003c\/p\u003e \u003cp\u003e3.6.2 Optimizing FOU Parameters 114\u003c\/p\u003e \u003cp\u003e3.7 Moving On 122\u003c\/p\u003e \u003cp\u003eAppendix 3A. Proof of Theorem 3.4 123\u003c\/p\u003e \u003cp\u003e3A.1 Inner-Bound Set [ul(), ur()] 123\u003c\/p\u003e \u003cp\u003e3A.2 Outer-Bound Set [ul(), ur()] 124\u003c\/p\u003e \u003cp\u003e4 Analytical Structure of Various Interval Type-2 Fuzzy PI and PD Controllers 131\u003c\/p\u003e \u003cp\u003e4.1 Introduction 131\u003c\/p\u003e \u003cp\u003e4.2 PID, PI, and PD Controllers and Their Relationships 134\u003c\/p\u003e \u003cp\u003e4.2.1 Two Forms of PID Controller—Position Form and Incremental Form 134\u003c\/p\u003e \u003cp\u003e4.2.2 PI and PD Controllers and Their Relationship 135\u003c\/p\u003e \u003cp\u003e4.3 Components of the Interval T2 Fuzzy PI and PD Controllers 136\u003c\/p\u003e \u003cp\u003e4.4 Mamdani Fuzzy PI and PD Controllers—Configuration 1 140\u003c\/p\u003e \u003cp\u003e4.4.1 Fuzzy PI Controller Configuration 140\u003c\/p\u003e \u003cp\u003e4.4.2 Method for Deriving the Analytical Structure 144\u003c\/p\u003e \u003cp\u003e4.5 Mamdani Fuzzy PI and PD Controllers—Configuration 2 154\u003c\/p\u003e \u003cp\u003e4.6 Mamdani Fuzzy PI and PD Controllers—Configuration 3 162\u003c\/p\u003e \u003cp\u003e4.6.1 Fuzzy PI Controller Configuration 162\u003c\/p\u003e \u003cp\u003e4.6.2 Method for Deriving the Analytical Structure 165\u003c\/p\u003e \u003cp\u003e4.7 Mamdani Fuzzy PI and PD Controllers—Configuration 4 169\u003c\/p\u003e \u003cp\u003e4.7.1 Fuzzy PI Controller Configuration 169\u003c\/p\u003e \u003cp\u003e4.7.2 Method for Deriving the Analytical Structure 171\u003c\/p\u003e \u003cp\u003e4.8 TSK Fuzzy PI and PD Controllers—Configuration 5 181\u003c\/p\u003e \u003cp\u003e4.8.1 Fuzzy PI Controller Configuration 181\u003c\/p\u003e \u003cp\u003e4.8.2 Deriving the Analytical Structure 184\u003c\/p\u003e \u003cp\u003e4.9 Analyzing the Derived Analytical Structures 185\u003c\/p\u003e \u003cp\u003e4.9.1 Structural Connection with the Corresponding T1 Fuzzy PI Controller 186\u003c\/p\u003e \u003cp\u003e4.9.2 Characteristics of the Variable Gains of the T2 Fuzzy PI Controller 190\u003c\/p\u003e \u003cp\u003e4.10 Design Guidelines for the T2 Fuzzy PI and PD Controllers 194\u003c\/p\u003e \u003cp\u003e4.10.1 Determination of 1 and 2 Values 196\u003c\/p\u003e \u003cp\u003e4.10.2 Determination of the Remaining Nine Parameter Values 197\u003c\/p\u003e \u003cp\u003e4.11 Summary 198\u003c\/p\u003e \u003cp\u003eAppendix 4A 200\u003c\/p\u003e \u003cp\u003e5 Analysis of Simplified Interval Type-2 Fuzzy PI and PD Controllers 205\u003c\/p\u003e \u003cp\u003e5.1 Introduction 205\u003c\/p\u003e \u003cp\u003e5.2 Simplified Type-2 FLCs: Design, Computation, and Performance 206\u003c\/p\u003e \u003cp\u003e5.2.1 Structure of a Simplified IT2 FLC 207\u003c\/p\u003e \u003cp\u003e5.2.2 Output Computation 208\u003c\/p\u003e \u003cp\u003e5.2.3 Computational Cost 209\u003c\/p\u003e \u003cp\u003e5.2.4 Genetic Tuning of FLC 210\u003c\/p\u003e \u003cp\u003e5.2.5 Performance 211\u003c\/p\u003e \u003cp\u003e5.2.6 Discussions 216\u003c\/p\u003e \u003cp\u003e5.3 Analytical Structure of Interval T2 Fuzzy PD and PI Controller 221\u003c\/p\u003e \u003cp\u003e5.3.1 Configuration of Interval T2 Fuzzy PD and PI Controller 221\u003c\/p\u003e \u003cp\u003e5.3.2 Analysis of the Karnik–Mendel Type-Reduced IT2 Fuzzy PD Controller 227\u003c\/p\u003e \u003cp\u003e6.7 Robust Control Design 277\u003c\/p\u003e \u003cp\u003e6.7.1 System Description 277\u003c\/p\u003e \u003cp\u003e6.7.2 Disturbance Rejection Problem and Solution 280\u003c\/p\u003e \u003cp\u003e6.7.3 Robust Control Example 284\u003c\/p\u003e \u003cp\u003e6.8 Summary 285\u003c\/p\u003e \u003cp\u003eAppendix 285\u003c\/p\u003e \u003cp\u003e7 Looking into the Future 290\u003c\/p\u003e \u003cp\u003e7.1 Introduction 290\u003c\/p\u003e \u003cp\u003e7.2 William Melek and Hao Ying Look into the Future 290\u003c\/p\u003e \u003cp\u003e7.3 Hani Hagras Looks into the Future 293\u003c\/p\u003e \u003cp\u003e7.3.1 Nonsingleton IT2 FL Control 293\u003c\/p\u003e \u003cp\u003e7.3.2 zSlices-Based Singleton General T2 FL Control 299\u003c\/p\u003e \u003cp\u003e7.4 Woei Wan Tan Looks into the Future 306\u003c\/p\u003e \u003cp\u003e7.5 Jerry Mendel Looks into The Future 307\u003c\/p\u003e \u003cp\u003e7.5.1 IT2 FLC 307\u003c\/p\u003e \u003cp\u003e7.5.2 GT2 FLC 309\u003c\/p\u003e \u003cp\u003eAppendix A T2 FLC Software: From Type-1 to zSlices-Based General Type-2 FLCs 315\u003c\/p\u003e \u003cp\u003eA.1 Introduction 315\u003c\/p\u003e \u003cp\u003eA.2 FLC for Right-Edge Following 315\u003c\/p\u003e \u003cp\u003eA.3 Type-1 FLC Software 316\u003c\/p\u003e \u003cp\u003eA.3.1 Define and Set Up T1 FLC Inputs 316\u003c\/p\u003e \u003cp\u003eA.3.2 Define T1 FSs That Quantify Each Variable 316\u003c\/p\u003e \u003cp\u003eA.3.3 Define Logical Antecedents and Consequents for the FL Rules 318\u003c\/p\u003e \u003cp\u003eA.3.4 Define Rule Base of T1 FLC 318\u003c\/p\u003e \u003cp\u003eA.4 Interval T2 FLC Software 321\u003c\/p\u003e \u003cp\u003eA.4.1 Define and Set Up FLC Inputs 323\u003c\/p\u003e \u003cp\u003eA.4.2 Define IT2 FSs That Quantify Each Variable 323\u003c\/p\u003e \u003cp\u003eA.4.3 Define Logical Antecedents and Consequents for the FL Rules 323\u003c\/p\u003e \u003cp\u003eA.4.4 Define Rule Base of the IT2 FLC 323\u003c\/p\u003e \u003cp\u003eA.5 zSlices-Based General Type-2 FLC Software 327\u003c\/p\u003e \u003cp\u003eA.5.1 Define and Set Up FLC Inputs 327\u003c\/p\u003e \u003cp\u003eA.5.2 Define zSlices-Based GT2 FSs That Quantify Each Variable 327\u003c\/p\u003e \u003cp\u003eA.5.3 Define Logical Antecedents and Consequents for the FL Rules 335\u003c\/p\u003e \u003cp\u003eA.5.4 Define Rule Base of the GT2 FLC 335\u003c\/p\u003e \u003cp\u003eReferences 338\u003c\/p\u003e \u003cp\u003eIndex 347\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default 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