Table of Contents
Chapter 1. Problem Representations
1.2 World Representations at Different Granularities
1.3 The Acquisition of Different Grain-Size Worlds
1.4 The Relation Among Different Grain Size Worlds
1.5 Property-Preserving Ability
1.6 Selection and Adjustment of Grain-Sizes
Chapter 2. Hierarchy and Multi-Granular Computing
2.2 The Estimation of Computational Complexity
2.3 The Extraction of Information on Coarsely Granular Levels
2.4 Fuzzy Equivalence Relation and Hierarchy
2.5 The Applications of Quotient Space Theory
Chapter 3. Information Synthesis in Multi-Granular Computing
3.2 The Mathematical Model of Information Synthesis
3.4 The Synthesis of Topologic Structures
3.5 The Synthesis of Semi-Order Structures
3.6 The Synthesis of Attribute Functions
Chapter 4. Reasoning in Multi-Granular Worlds
4.2 The Relation Between Uncertainty and Granularity
4.3 Reasoning (Inference) Networks (1)
4.5 Operations and Quotient Structures
4.7 Fuzzy Reasoning Based on Quotient Space Structures
Chapter 5. Automatic Spatial Planning
5.1 Automatic Generation of Assembly Sequences
5.2 The Geometrical Methods of Motion Planning
5.3 The Topological Model of Motion Planning
5.4 Dimension Reduction Method
Chapter 6. Statistical Heuristic Search
6.1 Statistical Heuristic Search
6.2 The Computational Complexity
6.3 The Discussion of Statistical Heuristic Search
6.4 The Comparison between Statistical Heuristic Search and A∗ Algorithm
6.6 Statistical Inference and Hierarchical Structure
Chapter 7. The Expansion of Quotient Space Theory
7.1 Quotient Space Theory in System Analysis
7.2 Quotient Space Approximation and Second-Generation Wavelets
7.3 Fractal Geometry and Quotient Space Analysis
7.4 The Expansion of Quotient Space Theory
Addenda A. Some Concepts and Properties of Point Set Topology
Addenda B. Some Concepts and Properties of Integral and Statistical Inference