Abstract
Abstract in Chinese
Notation
Chapter 1 Introduction
1.1 A Survey for the Advances of Rough Set Theory
1.1.1 Introduction of Rough Set Theory and Its Development
1.1.2 Main Problems Studied in Rough Set Theory
1.2 Basic Concepts of Rough Set
1.2.1 Definition of Rough Set and Some Important Concepts
1.2.2 Characterized Description of Rough Set
1.2.3 Rough Membership Function
1.2.4 Reduction and Core of Knowledge
1.2.5 Dependency of Knowledge
1.2.6 Representation Methods of Knowledge
1.3 Main Work in This Paper
Chapter 2 New Methods for Measuring Fuzziness in Rough Set
2.1 Fuzziness in Rough Set
2.1.1 Concepts of Fuzziness
2.1.2 Fuzziness in Rough Set Based on Equivalence Relation
2.1.3 Two New Calculating Formulae of the Fuzziness in Rough Set
2.1.4 Generalized Fuzziness in Rough Set Based on General Binary Relation
2.2 Measures of Similarity Between Rough Sets
2.2.1 Concepts of Similarity
2.2.2 Similarity Between Rough Sets Based on Equivalence Relation
2.2.3 Generalized Similarity Between Rough Sets Based on General Binary Relation
2.3 Fuzziness Induced by Similarity Based on Equivalence Relation
Chapter 3 Extensions of Rough Set Based on Rough Membership Function
3.1 Rough Membership Function Representation of Pawlak Rough Set and Its Limitations
3.2 λ-Rough Set Based on Rough Membership Function
3.2.1 λ-Rough Set Based on Equivalence Relation
3.2.2 Generalized λ-Rough Set Based on General Binary Relation
3.3 (α,β)-Rough Set Based on Rough Membership Function
3.3.1 (α,β)-Rough Set Based on Equivalence Relation
3.3.2 Generalized(α,β)-Rough Set Based on General Binary Relation
Chapter 4 Rough Set and Its Produced Knowledge and Knowledge Granule
4.1 Characters of Knowledge Granule and Calculation of Knowledge Granulation
4.1.1 Characters of Knowledge Granule
4.1.2 Calculation of Knowledge Granulation
4.1.3 Relations Between Knowledge Granulation, Discernibility Degree and Entropy
4.2 Knowledge Granulation Representation of the Concepts and Operations in Rough Set Theory
4.3 Attribute Reduction Based on Knowledge Granulation Under Information Systems
4.3.1 Attribute Reduction of Information Systems
4.3.2 Knowledge Granulation of Information Systems
4.3.3 Attribute Significance of Information Systems
4.3.4 A Knowledge Granulation-based Algorithm for Attribute Reduction under Information Systems
4.4 Attribute Reduction Based on Knowledge Granulation Under Incomplete Information Systems
4.4.1 Basic Concepts of Incomplete Information Systems
4.4.2 Attribute Reduction of Incomplete Information Systems
4.4.3 Knowledge Granulation of Incomplete Information Systems
4.4.4 Attribute Significance of Incomplete Information Systems
4.4.5 A Knowledge Granulation-based Algorithm for Attribute Reduction under Incomplete Information Systems
Chapter 5 Inducing Rough Region and Inducing Rough Correlation Region of Rough Set
5.1 Concepts and Properties of Inducing Rough Region and Inducing Rough Correlation Region
5.1.1 Basic Inducing Rough Factor and Basic Inducing Rough Correlation Factor
5.1.2 Concepts and Properties of Inducing Rough Region and Inducing Rough Correlation Region
5.2 Definitions and Properties of Some Particular Rough Sets
5.3 Approximately Exact of Rough Problems in Rough Set
5.3.1 An Impact of the Structure Feature of Inducing Rough Region and Inducing Rough Correlation Region on the Accuracy of Classification
5.3.2 Approximately Exact Methods of Rough Problems
Conclusions
Bibliography
Acknowledgements
Papers Published and Research Projects Undertaken During Studying for the Doctorate
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