By Yu, Wen,. . 1 PDF (208 pages). , <P>List of Figures xi</p> <p>List of Tables xiii</p> <p>Preface xv</p> <p><b>1 Fuzzy Equations </b><b>1</b></p> <p>1.1 Introduction 1</p> <p>1.2 Fuzzy Equations 1</p> <p>1.3 Algebraic Fuzzy Equations 3</p> <p>1.4 Numerical Methods for Solving Fuzzy Equations 5</p> <p>1.4.1 Newton Method 5</p> <p>1.4.2 Steepest Descent Method 7</p> <p>1.4.3 Adomian Decomposition Method 8</p> <p>1.4.4 Ranking Method 9</p> <p>1.4.5 Intelligent Methods 10</p> <p>1.4.5.1 Genetic Algorithm Method 10</p> <p>1.4.5.2 Neural Network Method 11</p> <p>1.4.5.3 Fuzzy Linear Regression Model 14</p> <p>1.5 Summary 20</p> <p><b>2 Fuzzy Differential Equations </b><b>21</b></p> <p>2.1 Introduction 21</p> <p>2.2 Predictor-Corrector Method 21</p> <p>2.3 Adomian Decomposition Method 23</p> <p>2.4 Euler Method 23</p> <p>2.5 Taylor Method 25</p> <p>2.6 Runge-Kutta Method 25</p> <p>2.7 Finite Difference Method 26</p> <p>2.8 Differential Transform Method 28</p> <p>2.9 Neural Network Method 29</p> <p>2.10 Summary 36</p> <p><b>3 Modeling and Control Using Fuzzy Equations </b><b>39</b></p> <p>3.1 Fuzzy Modeling with Fuzzy Equations 39</p> <p>3.1.1 Fuzzy Parameter Estimation with Neural Networks 45</p> <p>3.1.2 Upper Bounds of the Modeling Errors 48</p> <p>3.2 Control with Fuzzy Equations 52</p> <p>3.3 Simulations 59</p> <p>3.4 Summary 67</p> <p><b>4 Modeling and Control Using Fuzzy Differential Equations </b><b>69</b></p> <p>4.1 Introduction 69</p> <p>4.2 Fuzzy Modeling with Fuzzy Differential Equations 69</p> <p>4.3 Existence of a Solution 72</p> <p>4.4 Solution Approximation using Bernstein Neural Networks 79</p> <p>4.5 Solutions Approximation using the Fuzzy Sumudu Transform 83</p> <p>4.6 Simulations 85</p> <p>4.7 Summary 99</p> <p><b>5 System Modeling with Partial Differential Equations </b><b>101</b></p> <p>5.1 Introduction 101</p> <p>5.2 Solutions using Burgers-Fisher Equations 101</p> <p>5.3 Solution using Wave Equations 106</p> <p>5.4 Simulations 109</p> <p>5.5 Summary 117</p> <p><b>6 System Control using Z-numbers </b><b>119</b></p> <p>6.1 Introduction 119</p> <p>6.2 Modeling using Dual Fuzzy Equations and Z-numbers 119</p> <p>6.3 Controllability using Dual Fuzzy Equations 124</p> <p>6.4 Fuzzy Controller 128</p> <p>6.5 Nonlinear System Modeling 131</p> <p>6.6 Controllability using Fuzzy Differential Equations 131</p> <p>6.7 Fuzzy Controller Design using Fuzzy Differential Equations and Z-number 135</p> <p>6.8 Approximation using a Fuzzy Sumudu Transform and Z-numbers 138</p> <p>6.9 Simulations 139</p> <p>6.10 Summary 151</p> <p>References 153</p> <p>Index 167</p> 9781119491514 | 1119491525

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