# Quotient Space Based Problem Solving

*Quotient Space Based Problem Solving*: A Theoretical Foundation of Granular Computing

Research results obtained by the authors form the basis of this volume. The motivation behind this research is the belief that more human-like characteristics in problem solving should be involved in a formal representation in order to achieve better performance for computer-based problem solvers. While much of the current material available is presented in the language of mathematics, including elementary topology, set theory and statistics, *Quotient Space Based Problem Solving* presents key concepts and techniques, including basic definitions and theorems in accessible, practical terms before the relevant discussions. Each topic is introduced by simple examples and applications. *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.

- 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.

**Table of Contents**

Chapter 1. Problem Representation

Chapter 2. Hierarchy and Multi-granular Computing

Chapter 3. Information Synthesis in Multi-granular Computing

Chapter 4. Reasoning in Multi-granular Computing

Chapter 5. Automatic Spatial Planning

Chapter 6. Statistical Heuristic Search

Chapter 7. 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

### Book Details

**Hardcover:**396 pages**Publisher:**Morgan Kaufmann (February 2014)**Language:**English**ISBN-10:**0124103871**ISBN-13:**978-0124103870