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
1.1 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
2.3 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 Completeness 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 234
Chapter 11 Credibilistic Processes 235
11.1 L-R Fuzzy Variable 235
11.2 Renewal Process 236
11.3 Renewal Reward Process 245
11.4 Bibliographical Notes 250
Bibliography 251
Appendix List of Frequently Used CDFs 271
Index 273