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基于商空间的问题求解 粒度计算的理论基础PDF|Epub|txt|kindle电子书版本网盘下载

基于商空间的问题求解 粒度计算的理论基础
  • 张铃，张钹著 著
  • 出版社： 北京：清华大学出版社
  • ISBN：9787302384953
  • 出版时间：2014
  • 标注页数：382页
  • 文件大小：56MB
  • 文件页数：394页
  • 主题词：商空间－研究

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图书目录

Chapter 1 Problem Representations1

1.1. Problem Solving1

1.1.1. Expert Consulting Systems2

1.1.2. Theorem Proving2

1.1.3. Automatic Programming2

1.1.4. Graphical Representation3

1.1.5. AND/OR Graphical Representation3

1.2. World Representations at Different Granularities5

1.2.1. The Model of Different Grain-Size Worlds5

1.2.2. The Definition of Quotient Space7

1.3. The Acquisition of Different Grain-Size Worlds8

1.3.1. The Granulation of Domain8

1.3.2. The Granulation by Attributes9

1.3.3. Granulation by Structures11

1.4. The Relation Among Different Grain Size Worlds13

1.4.1. The Structure of Multi-Granular Worlds13

1.4.2. The Structural Completeness of Multi-Granular Worlds15

1.5. Property-Preserving Ability21

1.5.1. Falsity-Preserving Principle21

1.5.2. Quotient Structure32

1.6. Selection and Adjustment of Grain-Sizes32

1.6.1. Mergence Methods33

Example 1.15 34

1.6.2. Decomposition Methods34

1.6.3. The Existence and Uniqueness of Quotient Semi-Order41

1.6.4. The Geometrical Interpretation of Mergence and Decomposition Methods42

1.7. Conclusions43

Chapter 2 Hierarchy and Multi-Granular Computing45

2.1. The Hierarchical Model45

2.2. The Estimation of Computational Complexity48

2.2.1. The Assumptions48

2.2.2. The Estimation of the Complexity Under Deterministic Models49

2.2.3. The Estimation of the Complexity Under Probabilistic Models54

2.3. The Extraction of Information on Coarsely Granular Levels62

2.3.1. Examples64

2.3.2. Constructing[f]Under Unstructured Domains65

2.3.3. Constructing[f]Under Structured Domains67

2.3.4. Conclusions77

2.4. Fuzzy Equivalence Relation and Hierarchy77

2.4.1. The Properties of Fuzzy Equivalence Relations77

2.4.2. The Structure of Fuzzy Quotient Spaces84

2.4.3. Cluster and Hierarchical Structure86

2.4.4. Conclusions88

2.5. The Applications of Quotient Space Theory88

2.5.1. Introduction88

2.5.2. The Structural Definition of Fuzzy Sets90

2.5.3. The Robustness of the Structural Definition of Fuzzy Sets95

2.5.4. Conclusions102

2.6. Conclusions102

Chapter 3 Information Synthesis in Multi-Granular Computing105

3.1. Introduction105

3.2. The Mathematical Model of Information Synthesis106

3.3. The Synthesis of Domains108

3.4. The Synthesis of Topologic Structures109

3.5. The Synthesis of Semi-Order Structures110

3.5.1. The Graphical Constructing Method of Quotient Semi-Order110

3.5.2. The Synthesis of Semi-Order Structures112

3.6. The Synthesis of Attribute Functions117

3.6.1. The Synthetic Principle of Attribute Functions117

3.6.2. Examples120

3.6.3. Conclusions126

Chapter 4 Reasoning in Multi-Granular Worlds129

4.1. Reasoning Models129

4.2. The Relation Between Uncertainty and Granularity133

4.3. Reasoning(Inference)Networks(1)135

4.3.1. Projection138

4.3.2. Synthesis140

4.3.3. Experimental Results146

4.4. Reasoning Networks(2)147

4.4.1. Modeling151

4.4.2. The Projection of AND/OR Relations152

4.4.3. The Synthesis of AND/OR Relations155

4.4.4. Conclusion160

4.5. Operations and Quotient Structures160

4.5.1. The Existence of Quotient Operations162

4.5.2. The Construction of Quotient Operations164

4.5.3. The Approximation of Quotient Operations172

4.5.4. Constraints and Quotient Constraints176

4.6. Qualitative Reasoning181

4.6.1. Qualitative Reasoning Models182

4.6.2. Examples182

4.6.3. The Procedure of Qualitative Reasoning186

4.7. Fuzzy Reasoning Based on Quotient Space Structures187

4.7.1. Fuzzy Set Based on Quotient Space Model187

4.7.2. Fuzzified Quotient Space Theory189

4.7.3. The Transformation of Three Different Granular Computing Methods190

4.7.4. The Transformation of Probabilistic Reasoning Models191

4.7.5. Conclusions191

Chapter 5 Automatic Spatial Planning193

5.1. Automatic Generation of Assembly Sequences194

5.1.1. Introduction194

5.1.2. Algorithms195

5.1.3. Examples199

5.1.4. Computational Complexity202

5.1.5. Conclusions204

5.2. The Geometrical Methods of Motion Planning205

5.2.1. Configuration Space Representation205

5.2.2. Finding Collision-Free Paths206

5.3. The Topological Model of Motion Planning207

5.3.1. The Mathematical Model of Topology-Based Problem Solving208

5.3.2. The Topologic Model of Collision-Free Paths Planning210

5.4. Dimension Reduction Method216

5.4.1. Basic Principle216

5.4.2. Characteristic Network221

5.5. Applications230

5.5.1. The Collision-Free Paths Planning for a Planar Rod231

5.5.2. Motion Planning for a Multi-Joint Arm237

5.5.3. The Applications of Multi-Granular Computing242

5.5.4. The Estimation of the Computational Complexity246

Chapter 6 Statistical Heuristic Search249

6.1. Statistical Heuristic Search251

6.1.1. Heuristic Search Methods251

6.1.2. Statistical Inference254

6.1.3. Statistical Heuristic Search256

6.2. The Computational Complexity259

6.2.1. SPA Algorithms259

6.2.2. SAA Algorithms262

6.2.3. Different Kinds of SA264

6.2.4. The Successive Algorithms266

6.3. The Discussion of Statistical Heuristic Search267

6.3.1. Statistical Heuristic Search and Quotient Space Theory267

6.3.2. Hypothesis I268

6.3.3. The Extraction of Global Statistics271

6.3.4. SA Algorithms279

6.4. The Comparison between Statistical Heuristic Search and A* Algorithm280

6.4.1. Comparison to A280

6.4.2. Comparison to Other Weighted Techniques283

6.4.3. Comparison to Other Methods292

6.5. SA in Graph Search294

6.5.1. Graph Search294

6.5.2. AND/OR Graph Search295

6.6. Statistical Inference and Hierarchical Structure296

Chapter 7 The Expansion of Quotient Space Theory299

7.1. Quotient Space Theory in System Analysis299

7.1.1. Problems300

7.1.2. Quotient Space Approximation Models300

7.2. Quotient Space Approximation and Second-Generation Wavelets303

7.2.1. Second-Generation Wavelets Analysis303

7.2.2. Quotient Space Approximation305

7.2.3. The Relation between Quotient Space Approximation and Wavelet Analysis309

7.3. Fractal Geometry and Quotient Space Analysis311

7.3.1. Introduction311

7.3.2. Iterated Function Systems311

7.3.3. Quotient Fractals312

7.3.4. Conclusions315

7.4. The Expansion of Quotient Space Theory315

7.4.1. Introduction315

7.4.2. Closure Operation-Based Quotient Space Theory315

7.4.3. Non-Partition Model-Based Quotient Space Theory320

7.4.4. Granular Computing and Quotient Space Theory324

7.4.5. Protein Structure Prediction-An Application of Tolerance Relations326

7.4.6. Conclusions331

7.5. Conclusions331

Addenda A:Some Concepts and Properties of Point Set Topology333

Addenda B:Some Concepts and Properties of Integral and Statistical Inference363

References375

Index381

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