可信性测度论-处理主观不确定性的现代方法论

Preface Symbols and Abbreviations Chapter 1 Credibility Measure Space 1.1 Ample Space 1.2 Fuzzy Vector 1.3 Credibility Measure 1.4 Credibility Distribution Function 1.5 Building Credibility Measure 1.6 Generating L-S Measures 1.7 Bibliographical Notes Chapter 2 Product Credibility Measure 2.1 Finite-Dimensional Product Space 2.2 Infinite-Dimensional Product Space 2.3 Existence of Credibility Measure Space 2.4 Arithmetic of Fuzzy Variables 2.5 Bibliographical Notes Chapter 3 Convergence of Approximation 3.1 Convergence Criteria 3.2 Convergence Relations 3.3 Approximation Techniques 3.4 Credibility Simulation 3.5 Critical Value Simulation 3.6 Bibliographical Notes Chapter 4 Credibilistic Independence 4.1 Marginal Credibility Distributions 4.2 Independence of Fuzzy Vectors 4.3 Linear Combinations of Fuzzy Variables 4.4 Independence of Fuzzy Events 4.5 Bibliographical Notes Chapter 5 Numerical Characteristics 5.1 Expected Value Operators 5.2 Independence Linearity 5.3 Dominated Convergence Theorems 5.4 Expected Value Simulation 5.5 Variance of Fuzzy Variable 5.6 Absolute Deviations 5.7 Spread of Fuzzy Variable 5.8 Relation between Var and Sp 5.9 Moment of Fuzzy Variable 5.10 Skewness and Kurtosis 5.11 Bibliographical Notes Chapter 6 Lr Space of Fuzzy Variables 6.1 Uniform Integrability 6.2 Important Inequalities 6.3 Completeness of Lr Space 6.4 Bibliographical Notes Chapter 7 Credibilistic Orders 7.1 Usual Credibilistic Order 7.2 Credibilistic Stop-Loss Order 7.3 Credibilistic Convex Order 7.4 Bibliographical Notes Chapter 8 Credibilistic Risk Measures 8.1 Value at Risk 8.2 Conditional Value at Risk 8.3 CVaR Computational Formulas 8.4 Bibliographical Notes Chapter 9 Credibilistic Comonotonicity 9.1 Comonotonic Set 9.2 Comonotonic Fuzzy Vector 9.3 Two-ary Fuzzy Vector 9.4 Bibliographical Notes Chapter 10 Credibilistic Laws 10.1 □-Independence 10.2 Definitions of Laws 10.3 Law of Large Numbers 10.4 Bibliographical Notes Chapter 11 Credibilistic Processes 11.1 L-R Fuzzy Variable 11.2 Renewal Process 11.3 Renewal Reward Process 11.4 Bibliographical Notes Bibliography Appendix List of Frequently Used CDFs Index