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Quotient Space Based Problem Solving - 1st Edition - ISBN: 9780124103870, 9780124104433

Quotient Space Based Problem Solving

1st Edition

A Theoretical Foundation of Granular Computing

Authors: Ling Zhang Bo Zhang
Hardcover ISBN: 9780124103870
eBook ISBN: 9780124104433
Imprint: Morgan Kaufmann
Published Date: 13th February 2014
Page Count: 396
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Quotient Space Based Problem Solving provides an in-depth treatment of hierarchical problem solving, computational complexity, and the principles and applications of multi-granular computing, including inference, information fusing, planning, and heuristic search.

    Key Features

    • Explains the theory of hierarchical problem solving, its computational complexity, and discusses the principle and applications of multi-granular computing
    • Describes a human-like, theoretical framework using quotient space theory, that will be of interest to researchers in artificial intelligence
    • Provides many applications and examples in the engineering and computer science area
    • Includes complete coverage of planning, heuristic search and coverage of strictly mathematical models


    Quotient Space Based Problem Solving is designed for graduate students, research fellows and technicians in Computer Science, especially Artificial Intelligence, and those concerned with computerized problem solving.

    Table of Contents


    Chapter 1. Problem Representations

    1.1 Problem Solving

    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

    1.7 Conclusions

    Chapter 2. Hierarchy and Multi-Granular Computing

    2.1 The Hierarchical Model

    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

    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 Domains

    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

    4.1 Reasoning Models

    4.2 The Relation Between Uncertainty and Granularity

    4.3 Reasoning (Inference) Networks (1)

    4.4 Reasoning Networks (2)

    4.5 Operations and Quotient Structures

    4.6 Qualitative Reasoning

    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

    5.5 Applications

    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

    6.5 SA in Graph Search

    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

    7.5 Conclusions

    Addenda A. Some Concepts and Properties of Point Set Topology

    Addenda B. Some Concepts and Properties of Integral and Statistical Inference




    No. of pages:
    © Morgan Kaufmann 2014
    13th February 2014
    Morgan Kaufmann
    Hardcover ISBN:
    eBook ISBN:

    About the Authors

    Ling Zhang

    Professor Ling Zhang is currently with the Department of Computer Science at Anhui University in Hefei, China. His main interests are artificial intelligence, machine learning, neural networks, genetic algorithms and computational intelligence.

    Affiliations and Expertise

    Professor, Department of Computer Science at Anhui University in Hefei, China

    Bo Zhang

    Professor Bo Zhang is currently with the Computer Science and Technology Department at Tsinghua University in Beijing, China, He is a Fellow of Chinese Academy of Sciences. His main research interests include artificial intelligence, robotics, intelligent control and pattern recognition. He has published over 150 papers and 3 monographs in these fields.

    Affiliations and Expertise

    Professor, Computer Science and Technology Department at Tsinghua University in Beijing, China


    "The entire book is devoted to formalize and automate...a theory of granular computing, which is essentially based on quotient spaces." --Zentralblatt MATH

    "... aimed primarily at graduate students (and academicians) with strong mathematical maturity and an interest in mathematical modeling in the fields around artificial intelligence (AI)." --Computing Reviews, November 2014

    Ratings and Reviews