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可信性測度論-處理主觀不確定性的現代方法論 版權信息
- ISBN：9787030570864
- 條形碼：9787030570864 ; 978-7-03-057086-4
- 裝幀：一般膠版紙
- 冊數：暫無
- 重量：暫無
- 所屬分類：>>
可信性測度論-處理主觀不確定性的現代方法論 內容簡介
可信性測度論是處理主觀不確定性的一種常用數學分析工具，在實際決策問題中存在著廣泛的應用。劉彥奎著的《可信性測度論--處理主觀不確定性的現代方法論(英文版)》主要目的是介紹這一廣義測度理論近15年的發展狀況。全書共分十一章分別介紹可信性測度空間公理化體系、乘積可信性測度理論、逼近方法與收斂模式、模糊向量的獨立性、模糊變量的各種數字特征、一致可積與Lr空間的完備性、可信性排序、可信性風險度量、可信性同單調、可信性大數定律以及可信性過程等。
可信性測度論-處理主觀不確定性的現代方法論 目錄
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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