定 價：58 元
叢書名：現(xiàn)代數(shù)學基礎(chǔ)叢書
- 作者：周麗華，任長春，王麗珍[著]
- 出版時間：2018/3/1
- ISBN：9787030316776
- 出 版 社：科學出版社
- 中圖法分類：R72
- 頁碼：120
- 紙張：
- 版次：1
- 開本：B5
影響圖是不確定環(huán)境中描述復雜決策問題的圖模型，它表達了變量間的依賴關(guān)系、條件獨立關(guān)系和決策者的偏好信息。目前，影響圖已成為一種流行的標準建模工具。然而，現(xiàn)實中的決策環(huán)境復雜多樣，在一些應(yīng)用中現(xiàn)有的影響圖還不足以滿足要求，因此有必要對它們進行擴展。本書主要介紹影響圖的擴展及應(yīng)用，包括針對建模無限制決策問題、涉及連續(xù)變量的決策問題、涉及非精確變量的決策問題及多Agent 決策問題等方面對影響圖的擴展，以及影響圖的評價算法和競爭對手私人信息的推測。影響圖的擴展有助于增強影響圖的表達能力，豐富影響圖的類型，提高影響圖的適用性，促進影響圖的發(fā)展，擴大影響圖的應(yīng)用領(lǐng)域
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Contents
Preface
Chapter1 Introduction 1
1.1 Motivations 1
1.2 Outline of the Book 2
Chapter2 Influence Diagrams 3
2.1 Introduction 3
2.2 Preliminary 3
2.3 Influence Diagrams 9
2.3.1 Th e graphical component of an ID 9
2.3.2 The numerical component of an ID 11
2.4 Conclusion 14
Chapter3 The Extensions of Influence Diagrams 15
3.1 Introduction 15
3.2 Unconstrained Influence Diagrams (UIDs) 17
3.3 Limited Memory Influence Diagrams (LIMIDs) 19
3.4 Mixtures of Truncated Exponentials Influence Diagrams (MTE IDs) 20
3.5 Possibilistic Influence Diagrams (PIDs) 22
3.6 Interval-Valued Influence Diagrams (IIDs) 25
3.6.1 Bound-limited weak conditional interval probability 29
3.6.2 Influence diagrams with interval-valued parameters (BIIDs) 32
3.7 Game Theory-Based Influence Diagrams (GIDs) 33
3.7.1 Game theory 34
3.7.2 Game theory-based influence diagrams (GIDs) 36
3.8 Game IDs with Interval-Valued Parameters (GBIIDs) 39
3.9 Conclusion 41
Chapter4 The Evaluation of Influence Diagrams 42
4.1 Introduction 42
4.2 The Concept of Evaluating IDs 43
4.3 Evaluating Standard IDs 46
4.3.1 Arc reversal (AR) 46
4.3.2 Variable elimination(VE) 51
4.3.3 Cooper's method (CM) 54
4.4 Evaluating Interval-Valued IDs 57
4.4.1 Operations for interval-valued potentials 57
4.4.2 Interval arc reversal (IAR) 57
4.4.3 Interval variable elimination (IVE) 62
4.4.4 Chance variable and arc reversal elimination in IIDs by linear programming 65
4.4.5 Interval Cooper's method (ICM) for evaluating BIIDs 69
4.5 Evaluating GIDs 79
4.5.1 Concepts 79
4.5.2 The design of the genetic algorithm 82
4.5.3 The algorithm for evaluating GIDs (EAGIDs) 84
4.6 Evaluating Game IDs with Interval-Valued Parameters (GBIIDs) 89
4.6.1 Solving games with interval-valued utilities 89
4.6.2 Computing strategy utilities for utility nodes shared by multiple decision makers 90
4.6.3 Selecting the strategy with maximal interval-valued expect utility 92
4.7 Conclusion 93
Chapter5 Applications of Influence Diagrams 95
5.1 Finding Optimal Strategies for a Decision Maker by a BIID 95
5.2 Applying Influence Diagrams to Infer Rival's Private Information 99
5.2.1 The type of rival's private information 100
5.2.2 Inferring rival's private information 102
5.2.3 Experiments 104
5.3 Conclusion 107
References 109
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