可信性测度论

可信性测度论是处理主观不确定性的一种常用数学分析工具，在实际决策问题中存在着广泛的应用。本书主要目的是介绍这一广义测度理论近15年的发展状况。全书共分十一章分别介绍可信性测度空间公理化体系、乘积可信性测度理论、逼近方法与收敛模式、模糊向量的独立性、模糊变量的各种数字特征、一致可积与Lr空间的完备性、可信性排序、可信性风险度量、可信性同单调、可信性大数定律以及可信性过程等。

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

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