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《基于商空间的问题求解:粒度计算的理论基础(英文版)》共分7章和2个附录。第1章讲述问题的描述方法，关键是不同粒度世界的描述。第2章讲述分层与多粒度计算，重点是其数学模型，多粒度计算与计算复杂性、模糊分析的关系，以及它的应用。第3章多粒度计算中信息合成的数学模型，并由此导出合成的原则和方法。第4章多粒度世界中的推理，包括推理模型，不确定性与粒度的关系，推理网络、定性推理与模糊推理等。第5章自动空间规划，包括装配序列的自动产生，运动规划中的几何与拓扑方法，降维法及其应用。第6章介绍统计启发式搜索方法，分析它的理论、计算复杂性、算法的实现，这种算法的特点及其与多粒度计算的关系。第7章商空间问题求解理论的推广，包括将理论推广到非等价关系，该理论与小波分析与分形几何的关系，以及在系统分析中的应用。最后，在附录中介绍若干与《基于商空间的问题求解:粒度计算的理论基础(英文版)》内容关系密切的数学内容，主要是统计推断与点集拓扑的某些概念和结论，供不熟悉这部分数学内容的读者阅读时参考。

 

Preface
Chapter 1 Problem Representations
1.1.Problem Solving
1.1.1.Expert Consulting Systems
1.1.2.Theorem Proving
1.1.3.Automatic Programming
1.1.4.Graphical Representation
1.1.5.AND／OR Graphical Representation
1.2.World Representations at Diffrent Granularities
1.2.1.The Model of Different Grain—Size Worlds
1.2.2.The Definition of Quotient Space
1.3.The Acquisition of Difierent Grain—Size Worlds
1.3.1.The Granulation of Domain
1.3.2.The Granulation by Attributes
1.3.3.Granulation by Structures
1.4.The Relation Among Different Grain Size Worlds
1.4.1.The Structure of Multi—Granular Worlds
1.4.2.The Structural Completeness of Multi—Granular Worlds
1.5.Property—Preserving Ability
1.5.1.Falsity—Preserving Principle
1.5.2.Quotient Structure
1.6.Selection and Adjustment of Grain—Sizes
1.6.1.Mergence Methods
Example 1.15
1.6.2.Decomposition Methods
1.6.3.The Existence and Uniqueness of Quotient Semi—Order
1.6.4.The Geometrical Interpretation of Mergence and Decomposition Methods
1.7.Conclusions
Chapter 2 Hierarchy and Multi—Granular Computing
2.1.The Hierarchical Model
2.2.The Estimation of Computational Complexity
2.2.1.The Assumptions
2.2.2.The Estimation of the Complexity Under Deterministic Models
2.2.3.The Estimation of the Complexity Under Probabilistic Models
2.3.The Extraction of Information on Coarsely Granular Levels
2.3.1.Examples
2.3.2.Constructing （f） Under Unstructured Domains
2.3.3.Constructing （f） Under Structured Domains
2.3.4.Conclusions
2.4.Fuzzy Equivalence Relation and Hierarchy
2.4.1.The Properties of Fuzzy Equivalence Relations
2.4.2.The Structure of Fuzzy Quotient Spaces
2.4.3.Cluster and Hierarchical Structure
2.4.4.Conclusions
2.5.The Applications of Quotient Space Theory
2.5.1.Introduction
2.5.2.The Structural Definition of Fuzzy Sets
2.5.3.The Robustness of the Structural Definition of Fuzzy Sets
2.5.4.Conclusions
2.6.Conclusions
Chapter 3 Information Synthesis in Multi—Granular Computing
3.1.Introduction
3.2.The Mathematical Model of Information Synthesis
3.3.The Synthesis of Domaias
3.4.The Synthesis of Topologic Structures
3.5.The Synthesis of Semi—Order Structures
3.5.1.The Graphical Constructing Method of Quotient Semi—Order
3.5.2.The Synthesis of Semi—Order Structures
3.6.The Synthesis of Attribute Functions
3.6.1.The Synthetic Principle of Attribute Functions
3.6.2.Examples
3.6.3.Conclusions
Chapter 4 Reasoning in Multi—Granular Worlds
4.1.Reasoning Models
4.2.The Relation Between Uncertainty and Granularity
4.3.Reasoning（Inference）Networks（1）
4.3.1.Projection
4.3.2.Synthesis
4.3.3.Experimental Results
4.4.Reasoning Networks（2）
4.4.1.Modeling
4.4.2.The Projection of AND／OR Relations
4.4.3.The Synthesis of AND／OR Relations
4.4.4.Conclusion
4.5.Operations and Quotient Structures
4.5.1.The Existence of Quotient Operations
4.5.2.The Construction of Quotient Operations
4.5.3.The Approximation of Quotient Operations
4.5.4.Constraints and Quotient Constraints
4.6.Qualitative Reasoning
4.6.1.Qualitative Reasoning Models
4.6.2.Examples
4.6.3.The Procedure of Qualitative Reasoning
4.7.Fuzzy Reasoning Based on Quotient Space Structures
4.7.1.Fuzzy Set Based on Quotient Space Model
4.7.2.Fuzzified Quotient Space Theory
4.7.3.The Transformation of Three Different Granular Computing Methods
4.7.4.The Transformation of Probabilistic Reasoning Models
4.7.5.Conclusions
Chapter 5 Automatic Spatial Planning
5.1.Automatic Generation of Assembly Sequences
5.1.1.Introduction
5.1.2.Algorithms
5.1.3.Examples
5.1.4.Computational Complexity
5.1.5.Conclusions
5.2 The Geometrical Methods of Motion Planning
5.2.1.Configuration Space Representation
5.2.2.Finding Collision—Free Paths
5.3.The Topological Model of Motion Planning
5.3.1.The Mathematical Model of Topology—Based Problem Solving
5.3.2.The Topologic Model of Collision—Free Paths Planning
5.4.Dimension Reduction Method
5.4.1.Basic Principle
5.4.2.Characteristic Network
5.5.Applications
5.5.1.The Collision—Free Paths Planning for a Planar Rod
5.5.2.Motion Planning for a Multi—Joint Arm
5.5.3.The Applications of Multi—Granular Computing
5.5.4.The Estimation of the Computational Complexity
Chapter 6 Statistical Heuristic Search
6.1.Statistical Heuristic Search
6.1.1.Heuristic Search Methods
6.1.2.Statistical Inference
6.1.3.Statistical Heuristic Search
6.2.The Computational Complexity
6.2.1.SPA Algorithms
6.2.2.SAA Algorithms
6.2.3.Different Kinds of SA
6.2.4.The Successive Algorithms
6.3.The Discussion of Statistical Heuristic Search
6.3.1.Statistical Heuristic Search and Quotient Space Theory
6.3.2.Hypothesis I..
6.3.3.The Extraction of Global Statistics
6.3.4.SA Algorithms
6.4.The Comparison between Statistical Heuristic Search and A* Algorithm
6.4.1.Comparison to A*
6.4.2.Comparison to Other Weighted Techniques
6.4.3.Comparison to Other Methods
6.5.SA in Graph Search
6.5.1.Graph Search
6.5.2.AND／OR Graph Search
6.6.Statistical Inference and Hierarchical Structure
Chapter 7 The Expansion of Quotient Space therory
7.1.Quotient Space Theory in System Analysis
7.1.1.Problems
7.1.2.Quotient Space Approximation Models
7.2.Quotient Space Approximation and Second—Generation Wavelets
7.2.1.Second—Generation Wavelets Analysis
7.2.2.Quotient Space Approximation
7.2.3.The Relation between Quotient Space Approximation and Wavelet Analysis
7.3.Fractal Geometry and Quotient Space Analysis
7.3.1.Introduction
7.3.2.Iterated Function Systems
7.3.3.Quotient Fractals
7.3.4.Conclusions
7.4.The Expansion of Quotient Space Theory
7.4.1.Introduction
7.4.2.Closure Operation—Based Quotient Space Theory
7.4.3.Non—Partition Model—Based Quotient Space Theory
7.4.The Expansion of Quotient Space Theory
7.4.5.Protein Structure Prediction—An Application of Tolerance Relations
7.4.6.Conclusions
7.5.Conclusions
Addenda A：Some Concepts and Properties of Point Set Topology
Addenda B：Some Concepts and Properties of Integral and Statistical Inference
References
Index

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