不完全信息系统及粗糙集理论 : 模型和属性约简

PartⅠ Indiscenubility Relation Based Rough Sets

Chapter 1 Indiscernibility Relation, Rough Sets and Information System

1.1 Pawlak's Rough Approximation

1.1.1 Rough Set

1.1.2 Uncertainty Measurements and Knowledge Granulation

1.1.3 Knowledge Reductions

1.1.4 Knowledge Dependency

1.2 Variable Precision Rough Set

1.2.1 Inclusion Error and Variable Precision Rough Set

1.2.2 Several Reducts in Variable Precision Rough Set

1.3 Multigranulation Rough Set

1.3.1 Optimistic Multigranulation Rough Set

1.3.2 Pessimistic Multigranulation Rough Set

1.3.3 Multigranulation Rough Memberships

1.4 Hierarchical Structures on Multigranulation Spaces

1.4.1 Definitions of Three Hierarchical Structures

1.4.2 Relationships Between HierarchicalStructures and Multigranulation Rough Sets

1.5 Information System

1.5.1 Information System and Rough Set

1.5.2 Rough Sets in Multiple-source Information Systems

1.5.3 Several Reducts in Decision System

1.6 Conclusions

References

PartⅡ Incompletelnformation Systems and Rough Sets

Chapter 2 Expansions of Rough Sets in Incomplete Information Systems

2.1 Tolerance Relation Based Rough Set Approach

2.1.1 Tolerance Relation andlts Reducts

2.1.2 Tolerance Relation Based Rough Set and Generalized Decision Reduct

2.2 Valued Tolerance Relation Based Rough Set Approach

2.2.1 Valued Tolerance Relation

2.2.2 Valued Tolerance Relation Based Fuzzy Rough Set

2.3 Maximal Consistent Block Based Rough Set Approach

2.3.1 Maximal Consistent Block and Its Reducts

2.3.2 Maximal Consistent Block Based Rough Set and Approximate Distribution Reducts

2.4 Descriptor Based Rough Set

2.4.1 Descriptor and Reduct Descriptor

2.4.2 Descriptor Based Rough Set and Generalized Decision Reduct of Descriptor

2.5 Similarity Relation Based Rough Set Approach

2.5.1 Similarity Relation and Similarity Based Rough Set

2.5.2 Approximate Distribution Reducts in Similarity Relation Based Rough Set

2.6 Difference Relation Based Rough Set Approach

2.6.1 Difference Relation and Its Reducts

2.6.2 Rough Set Based on Difference Relation

2.6.3 Approximate Distribution Reducts in Difference Relation Based Rough Set

2.7 Limited Tolerance Relation Based Rough Set Approach

2.7.1 Limited Tolerance Relation

2.7.2 Limited Tolerance Relation Based Rough Set

2.8 Characteristic Relation Based Rough Set Approach

2.8.1 Characteristic Relation and Characteristic Relation Based Rough Set

2.8.2 Approximate Distribution Reducts in Characteristic Relation Based Rough Set

2.9 Conclusions

References

Chapter 3 Neighborhood System and Rough Set in Incomplete Information System

3.1 Neighborhood System

3.1.1 From Granular Computing to Neighborhood System

3.1.2 Binary Neighborhood System

3.1.3 Covering and Neighborhood System

3.1.4 Fuzzy Neighborhood System

3.1.5 Neighborhood System and Topological Space

3.1.6 Knowledge Operation in Neighborhood System

3.2 Neighborhood System and Rough Approximations

3.2.1 Neighborhood System Based Rough Sets

3.2.2 Relationship Between Neighborhood System Based Rough Set And VPRS

3.2.3 Neighborhood System Based Rough Approximations in Incomplete Information System

3.3 Reducts Neighborhood Systems

3.3.1 Reducts Neighborhood Systems inlncomplete Information System

3.3.2 Neighborhood Systems Based Approximate Distribution Reducts

3.4 Conclusions

References

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PartⅢ Dominance-based Rough sets and incomplete information systems

PartⅣ Incomplete information systems and multigranulation rough sets

Incomplete Information System and Rough Set Theory： Models And Attribute Re-ductions provides evidence of present growth in the rough set approach to the incom-plete information system. The topics discussed in this book have received significant　　attentions in recent years because researchers can apply new tools for problem solv-ing. This book reflects a number of approaches those were either directly or indirectly begun by the seminal work on rough set by Zdzislaw Pawlak.　　It is well-know that the knowledge representation system or the so-called infor-mation system plays a crucial role in Pawlak's rough set theory.　Evidence of the growth of various rough set-based research streams can be found in the rough set databasel.　However， in many practical applications， since the difficulties of acquisi-tions of knowledge， incomplete instead of the complete information systems can be seen everywhere. Therefore， how to employ the rough set approach to deal with the incomplete information systems is very important to the development of the rough set theory.