Part Ⅰ Indiscernibility 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 Hierarchical Structures 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 Part Ⅱ Incomplete Information 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 and Its 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 in Incomplete Information System 3.3.2 Neighborhood Systems Based Approximate Distribution Reducts 3.4 Conclusions References Part Ⅲ Dominance-based Rough Sets and Incomplete Information Systems Chapter 4 Dominance-based Rough Sets in “*“ Incomplete Information System 4.1 Dominance-based Rough Set 4.2 Expanded Dominance-based Rough Set in Incomplete Information System with “*“ Unknown Values 4.3 Valued Dominance-based Fuzzy Rough Set Approach 4.3.1 Valued Dominance Relation 4.3.2 Fuzzy Rough Approximations 4.3.3 Extraction of Decision Rules 4.4 ↑and↓ Descriptors and Certain Rules 4.4.1 Definition of ↑and↓ Descriptors 4.4.2 Reduct of ↑and↓ Descriptors 4.4.3 ↑and↓ Certain Rules 4.4.4 Optimal ↑and↓ Certain Rules 4.4.5 An Illustrative Example 4.5 Limited Dominance-based Rough Set Approach 4.5.1 Limited Dominance-based Rough Set 4.5.2 Comparisons Between Expanded and Limited Dominance-based Rough Sets 4.6 Conclusions References Chapter 5 Dominance-based Rough Sets in “?“ Incomplete Information System 5.1 Similarity Dominance Relation 5.1.1 Definition of Similarity Dominance Relation 5.1.2 Reducts of Similarity Dominance Relations 5.2 Similarity Dominance-based Rough Set and Approximate Distribution Reducts 5.2.1 Similarity Dominance-based Rough Set 5.2.2 Approximate Distribute Reducts in Similarity Dominance-based Rough Set 5.3 Similarity Dominance-based Rough Sets in Fuzzy Decision System 5.3.1 Similarity Dominance-based Rough Fuzzy Set 5.3.2 Relative Approximate Distribution Reducts of Similarity Dominance-based Rough Fuzzy Set 5.4 Conclusions References Part Ⅳ Incomplete Information Systems and Multigranulation Rough Sets Chapter 6 Multigranulation Rough Sets in Incomplete Information System 6.1 Tolerance Relations Based Multigranulation Rough Sets 6.1.1 Optimistic and Pessimistic Tolerance Relations Based Multigranulation Rough Sets 6.1.2 Properties of Multigranulation Rough Sets Based on Tolerance Relations 6.1.3 Comparisons Among Several Rough Sets 6.1.4 Approximation Distribution Reducts in Tolerance Relations Based Multigranulation Rough Sets 6.2 Similarity Relations Based Multigranulation Rough Sets 6.2.1 Optimistic and Pessimistic Similarity Relations Based Multigranulation Rough Sets 6.2.2 Properties of Multigranulation Rough Sets Based on Similarity Relations 6.2.3 Comparisons Among Several Rough Sets 6.2.4 Approximate Distribution Reducts in Similarity Relations Based Multigranulation Rough Sets 6.3 Conclusions References Glossary Index
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