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醉染图书可信测度论9787030570864
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Preface Symbols and Abbreviations Chapter 1 Credibility Measure Space 1 1.1 Ample Space 1 1.2 Fuzzy Vector 2 1.3 Credibility Measure 4 1.4 Credibility Distribution Function 11 1.5 Building Credibility Measure 12 1.6 Generating L-S Measures 21 1.7 Bibliographical Notes 26 Chapter 2 Product Credibility Measure 30 2.1 Finite-Dimensional Product Space 30 2.2 Infinite-Dimensional Product Space 35 . Existence of Credibility Measure Space 45 2.4 Arithmetic of Fuzzy Variables 54 2.5 Bibliographical Notes 59 Chapter 3 Convergence of Approximation 61 3.1 Convergence Criteria 61 3.2 Convergence Relations 64 3.3 Approximation Techniques 65 3.4 Credibility Simulation 70 3.5 Critical Value Simulation 77 3.6 Bibliographical Notes 81 Chapter 4 Credibilistic Independence 84 4.1 Marginal Credibility Distributions 84 4.2 Independence of Fuzzy Vectors 90 4.3 Linear Combinations of Fuzzy Variables 99 4.4 Independence of Fuzzy Events 101 4.5 Bibliographical Notes 105 Chapter 5 Numerical Characteristics 107 5.1 Expected Value Operators 107 5.2 Independence Linearity 112 5.3 Dominated Convergence Theorems 118 5.4 Expected Value Simulation 124 5.5 Variance of Fuzzy Variable 129 5.6 Absolute Deviations 135 5.7 Spread of Fuzzy Variable 148 5.8 Relation between Var and Sp 155 5.9 Moment of Fuzzy Variable 158 5.10 Skewness and Kurtosis 165 5.11 Bibliographical Notes 166 Chapter 6 Lr Space of Fuzzy Variables 168 6.1 Uniform Integrability 168 6.2 Important Inequalities 172 6.3 Comleess of Lr Space 173 6.4 Bibliographical Notes 179 Chapter 7 Credibilistic Orders 180 7.1 Usual Credibilistic Order 180 7.2 Credibilistic Stop-Loss Order 188 7.3 Credibilistic Convex Order 190 7.4 Bibliographical Notes 193 Chapter 8 Credibilistic Risk Measures 194 8.1 Value at Risk 194 8.2 Conditional Value at Risk 206 8.3 CVaR Computational Formulas 210 8.4 Bibliographical Notes 213 Chapter 9 Credibilistic Comonotonicity 215 9.1 Comonotonic Set 215 9.2 Comonotonic Fuzzy Vector 215 9.3 Two-ary Fuzzy Vector 221 9.4 Bibliographical Notes 224 Chapter 10 Credibilistic Laws 225 10.1 Independence 225 10.2 Definitions of Laws 227 10.3 Law of Large Numbers 229 10.4 Bibliographical Notes 4 Chapter 11 Credibilistic Processes 5 11.1 L-R Fuzzy Variable 5 11.2 Renewal Process 11.3 Renewal Reward Process 245 11.4 Bibliographical Notes 250 Bibliography 251 Appendix List of Frequently Used CDFs 271 Index 273
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