不完全信息系統(tǒng)及粗糙集理論

內(nèi)容概要

　　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.

書籍目錄

Part I Indiscernibility Relation Based Rough SetsChapter 1 indiscernibility Relation, Rough Sets and Information System1.1 Pawlak's Rough Approximation1.1.1 Rough Set1.1.2 Uncertainty Measurements and Knowledge Granulation1.1.3 Knowledge Reductions1.1.4 Knowledge Dependency1.2 Variable Precision Rough Set1.2.1 Inclusion Error and Variable Precision Rough Set1.2.2 Several Reducts in Variable Precision Rough Set1.3 Multigranulation Rough Set1.3.1 Optimistic Multigranulation Rough Set1.3.2 Pessimistic Multigranulation Rough Set1.3.3 Multigranulation Rough Memberships1.4 Hierarchical Structures on Multigranulation Spaces1.4.1 Definitions of Three Hierarchical Structures1.4.2 Relationships Between Hierarchical Structures and Multigranulation Rough Sets1.5 Information System1.5.1 Information System and Rough Set1.5.2 Rough Sets in Multiple-source Information Systems1.5.3 Several Reducts in Decision System1.6 ConclusionsReferencesPart II Incomplete Information Systems and Rough SetsChapter 2 Expansions of Rough Sets in Incomplete Information Systems..2.1 Tolerance Relation Based Rough Set Approach2.1.1 Tolerance Relation and Its Reducts2.1.2 Tolerance Relation Based Rough Set and Generalized Decision Reduct2.2 Valued Tolerance Relation Based Rough Set Approach2.2.1 Valued Tolerance Relation2.2.2 Valued Tolerance Relation Based Fuzzy Rough Set2.3 Maximal Consistent Block Based Rough Set Approach2.3.1 Maximal Consistent Block and Its Reducts2.3.2 Maximal Consistent Block Based Rough Set and Approximate Distribution Reducts2.4 Descriptor Based Rough Set2.4.1 Descriptor and Reduct Descriptor2.4.2 Descriptor Based Rough Set and Generalized Decision Reduct of Descriptor2.5 Similarity Relation Based Rough Set Approach2.5.1 Similarity Relation and Similarity Based Rough Set2.5.2 Approximate Distribution Reducts in Similarity Relation Based Rough Set2.6 Difference Relation Based Rough Set Approach2.6.1 Difference Relation and Its Reducts2.6.2 Rough Set Based on Difference Relation2.6.3 Approximate Distribution Reducts in Difference Relation Based Rough Set2.7 Limited Tolerance Relation Based Rough Set Approach2.7.1 Limited Tolerance Relation2.7.2 Limited Tolerance Relation Based Rough Set2.8 Characteristic Relation Based Rough Set Approach2.8.1 Characteristic Relation and Characteristic Relation Based Rough Set2.8.2 Approximate Distribution Reducts in Characteristic Relation Based Rough Set2.9 ConclusionsReferencesChapter 3 Neighborhood System and Rough Set in Incomplete Information System3.1 Neighborhood System3.1.1 From Granular Computing to Neighborhood System3.1.2 Binary Neighborhood System3.1.3 Covering and Neighborhood System3.1.4 Fuzzy Neighborhood System3.1.5 Neighborhood System and Topological Space3.1.6 Knowledge Operation in Neighborhood System3.2 Neighborhood System and Rough Approximations3.2.1 Neighborhood System Based Rough Sets3.2.2 Relationship Between Neighborhood System Based Rough Set and VPRS3.2.3 Neighborhood System Based Rough Approximations in Incomplete Information System3.3 Reducts Neighborhood Systems3.3.1 Reducts Neighborhood Systems in Incomplete Information System3.3.2 Neighborhood Systems Based Approximate Distribution Reducts3.4 ConclusionsReferencesPart III Dominance-based Rough Sets and Incomplete Information SystemsChapter 4 Dominance-based Rough Sets in "," Incomplete Information SystemChapter 5 Dominance-based Rough Sets in "？" Incomplete Information SystemPart IV Incomplete Information Systems and Multigranulation Rough SetsChapter 6 Multigranulation Rough Sets in Incomplete Information System

章節(jié)摘錄

插圖：Abstract  Pawlak's rough set model, was firstly constructed on the basis of an indiscemibility relation. Such an indiscernibility relation is an intersection of some equivalence relations in knowledge base and then it is also an equivalence relation.This chapter introduced the basic concepts of Pawlak's rough set, Ziarko's variable precision rough set and Qian's multigranulation rough sets. These models were all proposed on the basis of indiscernibility relation. Variable precision rough set generalizes classical rough approximation by introducing a threshold ft. Such fl value represents a bound on the conditional probability of an equivalence class, which are classified into the target concept. Multigranulation rough set uses a family of the indiscernibility relation instead of a single one to construct rough approximation. In multigranulation rough set approach, the optimistic and pessimistic multigranulation rough sets are two basic models.

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