Quotient Space Based Problem Solving

1st Edition

A Theoretical Foundation of Granular Computing

Print ISBN: 9780128103098
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 St


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    © Morgan Kaufmann 2014
    Morgan Kaufmann
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    "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