Transactions on Rough Sets XIII
Springer (Publisher)
Published on 28. January 2011
VIII, 277 pages
978-3-642-18302-7 (ISBN)
Description
The LNCS journal Transactions on Rough Sets is devoted to the entire spectrum of rough sets related issues, from logical and mathematical foundations, through all aspects of rough set theory and its applications, such as data mining, knowledge discovery, and intelligent information processing, to relations between rough sets and other approaches to uncertainty, vagueness, and incompleteness, such as fuzzy sets and theory of evidence.
Volume XIII contains 14 papers which introduce a number of new advances in both the foundations and the applications of rough sets. These are mathematical structures of generalized rough sets in infinite universes, approximations of arbitrary binary relations, and attribute reduction in decision-theoretic rough sets. Methodological advances introduce rough set-based and hybrid methodologies for learning theory, attribution reduction, decision analysis, risk assessment, and data mining tasks such as classification and clustering. In addition, this volume contains regular articles on mining temporal software metrics data, C-GAME discretization method, perceptual tolerance intersection as an example of a near set operation and compression of spatial data with quadtree structures.
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Content
- Title Page
- Preface
- Table of Contents
- Bit-Vector Representation of Dominance-Based Approximation Space
- Introduction
- Related Concepts
- Information Systems and Rough Sets
- Dominance-Based Rough Sets
- Indexed Blocks as Granules
- Approximations by Neighborhoods of Indexed Blocks
- Computing Indexed Blocks from MCDT
- Based on Single Criterion
- Based on Multiple Criteria
- Generate Decision Rules from Indexed Blocks
- Bit-Vector Encodings of Indexed Blocks
- Decision Rules
- Conclusions
- References
- Approximations of Arbitrary Binary Relations by Partial Orders: Classical and Rough Set Models
- Introduction
- Intuition and Motivation: Pairwise Comparisons Non-numerical Ranking
- Relations and Partial Orders
- Inclusion Property and Equivalence w.r.t. a Given Relation
- Approximating Relations by Partial Orders
- Approximation with Partially Ordered Kernel
- Classical Rough Relations
- Property-Driven Rough Approximations of Binary Relations
- Property-Driven Rough Partial Order Approximations of Arbitrary Relations
- Compound Properties and Mixed Approximations
- Final Comment
- References
- Hybridization of Rough Sets and Statistical Learning Theory
- Introduction
- Probabilistic Model
- Complete Information Systems
- Rough Set Theory
- Extended Approximations
- Rule Induction Algorithm
- Tests
- Decision Rules Extraction
- Conclusions
- References
- Fuzzy-Rough Nearest Neighbour Classification
- Introduction
- Hybridization of Rough Sets and Fuzzy Sets
- Rough Set Theory
- Fuzzy Set Theory
- Fuzzy-Rough Set Theory
- Fuzzy-Rough Classification
- Fuzzy Nearest Neighbour Classification
- Fuzzy-Rough Nearest Neighbour (FRNN) Algorithm
- Experimentation
- Classification
- Prediction
- Conclusion and Future Work
- References
- Efficient Mining of Jumping Emerging Patterns with Occurrence Counts for Classification
- Introduction
- Previous Work
- Emerging Patterns
- Jumping Emerging Patterns with Occurrence Counts
- A Semi-Naïve Mining Algorithm
- Border-Based Mining Algorithm
- Algorithm Optimizations
- Discovering occJEPs
- Performing Classification
- Experimental Results
- Image Dataset
- Text Dataset
- Conclusions and Future Work
- References
- Rough Entropy Hierarchical Agglomerative Clustering in Image Segmentation
- Introduction
- Hierarchical Clustering
- Hierarchical Agglomerative Clustering
- Clustering Quality Measures
- Rough Entropy Hierarchical Clustering
- Rough Entropy Hierarchical Agglomerative Clustering
- Group Cluster Representation
- Cluster Group Similarity Measures
- Rough Entropy Measures
- Rough Entropy Weighting
- Linkage Strategies Example
- Experimental Setup and Results
- Introduction
- Image Datasets
- Text Image Experiments
- Berkeley Images Experiments
- Conclusions and Future Research
- References
- Software Defect Prediction Based on Source Code Metrics Time Series
- Introduction
- Defect Prediction
- Software Metrics
- Metrics Time Series
- Remainder of the Paper
- Motivation
- Metrics Used
- Metric Descriptions
- The Algorithm
- Notation and Definitions
- Experiment Steps
- The Experiment
- Data
- Interesting Rules
- Conclusion
- Prediction Quality
- Structure of Inferred Rules
- Related Work
- Future Work
- References
- Risk Assessment in Granular Environments
- Introduction
- Granularity and Granular Computing
- Risk in Statistical Learning Theory
- Approximation of Loss Function and Its Integral
- The Rough Set Case
- The Fuzzy Set Case
- Classifiers, Neighbourhoods and Granulation
- Summary and Conclusion
- References
- Core-Generating Discretization for Rough Set Feature Selection
- Introduction
- Preliminary Concepts
- Rough Set Theory
- Discretization Problems
- Constraint Satisfaction Problems
- Rough Set Feature Selection for Continuous Datasets
- Core-Generating Discretization
- Core-Generating vs. Non-core-Generating: An Axis
- Core Size and Core-Generating Objects
- Core-Generating Sets of Cuts
- Properties of a Core-Generating Set of Cuts
- Formulating S-Core-Generating Discretization Using Constraint Satisfaction
- The CSP Model
- Core-Generating Approximate Minimum Entropy Discretization
- Degree of Approximation of Minimum Entropy
- Computing a C-GAME Set of Cuts by Solving a CSOP
- Effect of Different Cores on Classification Performances of Reducts
- C-GAME Discretization Algorithm
- Performance Evaluation
- Ten-Fold Cross Validation
- Conclusion
- References
- Perceptual Tolerance Intersection
- Introduction
- Tolerance Relations
- Tolerance Intersection of Sets
- Near Sets and Perceptual Tolerance Relations
- Practical Application of Near Sets in Image Analysis
- Perceptual Intersection of Sets and Perceptual Similarity Measures
- Conclusion
- References
- Some Mathematical Structures of Generalized Rough Sets in Infinite Universes of Discourse
- Introduction
- Related Works
- Construction of Generalized Rough Approximation Operators
- Topological Spaces and Rough Approximation Operators
- Basic Concepts of Topological Spaces
- From Approximation Spaces to Topological Spaces
- From Topological Spaces to Approximation Spaces
- Axiomatic Characterizations of Rough Approximation Operators
- Rough Set Algebras in Infinite Universes of Discourse
- Serial RSAs
- Reflexive RSAs
- Symmetric RSAs
- Transitive RSAs
- Euclidean RSAs
- Serial and Symmetric RSAs
- Serial and Transitive RSAs
- Serial and Euclidean RSAs
- Symmetric and Transitive RSAs
- Symmetric and Euclidean RSAs
- Transitive and Euclidean RSAs
- Topological RSAs
- Measurable Structures of Rough Set Algebras
- Belief Structures of Rough Sets
- Belief Structures and Belief Functions on Infinite Universes of Discourse
- Relationship between Belief Functions and Rough Sets on Infinite Universes of Discourse
- Properties of Belief and Plausibility Functions on Infinite Universes of Discourse
- Conclusion
- References
- Quadtree Representation and Compression of Spatial Data
- Introduction
- Quadtrees and Rough Sets
- Overview of Quadtrees
- Alternative Types of Quadtree Representation
- Quadtree Approximation Methods
- Quadtrees and Rough Sets
- Algorithm Design
- Problem Analysis
- Influential Factors of Quadtree Cost
- Significance of Quadtree Root Node Choice
- Criteria for the Root Node Selection
- Choosing a Root Node
- Empirical Results
- Outlook
- References
- Solving the Attribute Reduction Problem with Ant Colony Optimization
- Introduction
- The Attribute Reduction Problem
- Information Tables
- Discernibility Matrices
- Discernibility Function
- ACO for Attribute Reduction
- Attribute-Graph for Attribute Reduction
- Pheromone Trails and Heuristic Information
- Framework of a Basic ACO Algorithm
- R-Graph to Solve MARP with ACO
- Constraint Satisfaction Problem
- R-Graph for Attribute Reduction
- Constructing a Solution
- Model Comparison
- Discernibility Matrix Simplification
- Minimal Reduction Space
- Absorption Operator
- Cutting Operator
- Description of Algorithm R-ACO
- Construction Graph and Initialization
- Selection of a Variable
- Choice of a Value
- Pheromone Updating
- Termination Conditions
- Experimental Results
- EQ6100 Engine Fault Diagnosis Data Set
- Standard UCI Data Sets
- Conclusion
- References
- A Note on Attribute Reduction in the Decision-Theoretic Rough Set Model
- Introduction
- The Decision-Theoretic Rough Set Model
- Probabilistic Approximations and Regions
- Decision Making
- Monotocity Property of the Regions
- Definitions and Interpretations of Attribute Reduction
- An Interpretation of Region Preservation in the Pawlak Model
- Difficulties with the Interpretations of Region Preservation in the Decision-Theoretic Model
- Constructing Decision-Preserved Reducts in the Decision-Theoretic Model
- Constructing Region-Preserved Reducts in the Decision-Theoretic Model
- Conclusion
- References
- Author Index
