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Quotient Space Based Problem Solving - A Theoretical Foundation of Granular Computing
of: Ling Zhang, Bo Zhang
Elsevier Reference Monographs, 2014
ISBN: 9780124104433 , 397 Pages
Format: PDF, ePUB, Read online
Copy protection: DRM
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Quotient Space Based Problem Solving - A Theoretical Foundation of Granular Computing
Front Cover
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Quotient Space Based Problem Solving: A Theoretical Foundation of Granular Computing
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Copyright
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Contents
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Preface
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Chapter 1 - Problem Representations
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1.1 Problem Solving
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1.2 World Representations at Different Granularities
20
1.3 The Acquisition of Different Grain-Size Worlds
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1.4 The Relation Among Different Grain Size Worlds
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1.5 Property-Preserving Ability
36
1.6 Selection and Adjustment of Grain-Sizes
47
Example 1.15
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1.7 Conclusions
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Chapter 2 - Hierarchy and Multi-Granular Computing
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2.1 The Hierarchical Model
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2.2 The Estimation of Computational Complexity
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2.3 The Extraction of Information on Coarsely Granular Levels
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2.4 Fuzzy Equivalence Relation and Hierarchy
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2.5 The Applications of Quotient Space Theory
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2.6 Conclusions
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Chapter 3 - Information Synthesis in Multi-Granular Computing
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3.1 Introduction
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3.2 The Mathematical Model of Information Synthesis
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3.3 The Synthesis of Domains
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3.4 The Synthesis of Topologic Structures
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3.5 The Synthesis of Semi-Order Structures
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3.6 The Synthesis of Attribute Functions
132
Chapter 4 - Reasoning in Multi-Granular Worlds
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4.1 Reasoning Models
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4.2 The Relation Between Uncertainty and Granularity
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4.3 Reasoning (Inference) Networks (1)
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4.4 Reasoning Networks (2)
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4.5 Operations and Quotient Structures
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4.6 Qualitative Reasoning
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4.7 Fuzzy Reasoning Based on Quotient Space Structures
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Chapter 5 - Automatic Spatial Planning
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5.1 Automatic Generation of Assembly Sequences
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5.2 The Geometrical Methods of Motion Planning
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5.3 The Topological Model of Motion Planning
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5.4 Dimension Reduction Method
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5.5 Applications
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Chapter 6 - Statistical Heuristic Search
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6.1 Statistical Heuristic Search
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6.2 The Computational Complexity
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6.3 The Discussion of Statistical Heuristic Search
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6.4 The Comparison between Statistical Heuristic Search and A* Algorithm
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6.5 SA in Graph Search
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6.6 Statistical Inference and Hierarchical Structure
311
Chapter 7 - The Expansion of Quotient Space Theory
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7.1 Quotient Space Theory in System Analysis
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7.2 Quotient Space Approximation and Second-Generation Wavelets
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7.3 Fractal Geometry and Quotient Space Analysis
326
7.4 The Expansion of Quotient Space Theory
330
7.5 Conclusions
346
Addenda A - Some Concepts and Properties of Point Set Topology
348
A.1 Relation and Mapping
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A.2 Topology Space
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A.3 Separability Axiom
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A.4 Countability Axiom
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A.5 Compactness
361
A.6 Connectedness
364
A.7 Order-Relation, Galois Connected and Closure Space
368
Addenda B - Some Concepts and Properties of Integral and Statistical Inference
378
B.1 Some Properties of Integral
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B.2 Central Limit Theorem
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B.3 Statistical Inference
384
References
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Index
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