Note: Intro -- Preface -- RSKT 2006 Conference Committee -- Table of Contents -- Author Index.

Note: Intro -- Preface -- Contents -- List of Figures -- 1 Computational Proximity -- 1.1 Computational Proximity Framework -- 1.2 Points, Regions, Connectedness and Point-Free Geometry -- 1.3 Choice of Probe -- 1.4 Proximities -- 1.5 Di Concilio Strong Contact -- 1.6 Strongly Far Proximity -- 1.7 Convexity Structures -- 1.8 Descriptive Proximity -- 1.9 Descriptive Strong Proximity -- 1.10 Nerves -- 1.11 Voronoï Diagrams and Mesh Nerves -- 1.12 Origins, Variations and Applications of Voronoï Diagrams -- 1.13 Mesh Nerves on a Digital Image -- 1.14 Singer Needle Tip Image Mesh: A Step Toward Object Recognition -- 1.15 Topological Spaces: Setting for Computational Proximity -- 1.16 Connectedness and Strongly Near Connectedness -- 1.17 Connected and Strongly Connected Mesh Nerves -- 1.18 Boundedness, Bornology and Bornological Nerves -- 1.19 Proximal Boundedness, Strong Proximal Boundedness -- 1.20 Local Proximity Spaces and Local Strong Proximity Spaces -- References -- 2 Proximities Revisited -- 2.1 Cech Proximity -- 2.2 Cech Closure of a Set -- 2.3 Near Edge Sets -- 2.4 Lodato Proximity -- 2.5 Descriptive Lodato Proximity -- 2.6 Delaunay Triangulation -- 2.7 Voronoï Diagrams Revisited -- 2.7.1 Sites -- 2.8 Some Results for Voronoï Regions -- 2.9 Dirichlet Tessellation Quality and Digital Image Quality -- 2.10 Tessellation Region Centroids -- 2.11 Centroid-Based Voronoï Mesh on an Image -- References -- 3 Distance and Proximally Continuous -- 3.1 Metrics and Metric Topology -- 3.2 Distances: Euclidean and Taxicab Metrics -- 3.3 Metric Proximity -- 3.4 Closeness Metric -- 3.5 Some Recent History of Near Sets -- 3.6 Descriptive Similarity Distance -- 3.7 Descriptively Near Sets Can Be Spatially Disjoint Sets -- 3.8 Neighbourhoods of Points in Euclidean Space -- 3.9 2D Picture Descriptive Neighbourhood of a Point. , 3.9.1 Unbounded Descriptive Neighbourhood of a Picture Point -- 3.9.2 Bounded Descriptive Neighbourhood of a Picture Point -- 3.9.3 Bounded Indistinguishable Descriptive Neighbourhood of a Picture Point -- 3.9.4 Unbounded Indistinguishable Descriptive Neighbourhood of a Picture Point -- References -- 4 Image Geometry and Nearness Expressions for Image and Scene Analysis -- 4.1 Image Geometry -- 4.1.1 Delaunay Triangulation -- 4.1.2 Voronoï Diagrams -- 4.2 Nearness Expressions: Basic Notions -- 4.3 Near and Strongly Near Sets Revisited -- 4.3.1 Lodato Proximity Revisited -- 4.3.2 Descriptive Lodato Proximity Revisited -- 4.3.3 Strong Proximity Revisited -- 4.3.4 Descriptive Strong Proximity Revisited -- 4.4 Di Concilio--Gerla Overlap Revisited -- 4.5 Wallman Proximity Revisited -- 4.6 Far and Strongly Far Sets Revisited -- References -- 5 Homotopic Maps, Shapes and Borsuk--Ulam Theorem -- 5.1 Antipodal Points and Hyperspheres -- 5.2 Borsuk--Ulam Theorem -- 5.3 Homotopic Maps and Deformation Retracts -- 5.4 Object Description, Structured Sets and Shape Features -- 5.4.1 Euclidean Feature Space -- 5.4.2 Feature Vectors -- 5.5 Strongly Proximal Object and Feature Spaces -- 5.6 Strong Proximal Borsuk--Ulam Theorem -- 5.7 Strong Proximal Region-Based Borsuk--Ulam Theorem -- 5.8 Complexes, Nuclei and Applied Homotopy -- 5.9 Strong Proximal Homotopy -- 5.10 Borsuk--Ulam Theorem Extended to Hyperbolic Surfaces by A. Tozzi -- References -- 6 Visibility, Hausdorffness, Algebra and Separation Spaces -- 6.1 Visibility -- 6.2 Separation Axioms -- 6.3 R0 Symmetric Space -- 6.4 Descriptive R0 Space -- 6.4.1 Near Sets in L-Proximity Spaces -- 6.4.2 Descriptive L-Proximity -- 6.4.3 Descriptive Proximity Space Revisited -- 6.5 T0 Anti-Symmetric Space -- 6.6 T1 Space -- 6.7 Hausdorff T2 Space -- 6.8 Hausdorffness and Visibility. , 6.9 Partial Descriptive Groupoids in Hausdorff Spaces -- 6.10 Set-Based Probes and Proximal Delaunay Groupoids -- 6.11 Voronoï Groupoids -- 6.12 T3 Space -- 6.13 T4 Space -- 6.14 Visual Set Patterns in Descriptive Separation Spaces -- 6.14.1 Visual Patterns in Descriptive T1 Spaces -- 6.14.2 Visual Patterns in Descriptive T2 Spaces -- 6.14.3 Set Pattern Generators -- References -- 7 Strongly Near Sets and Overlapping Dirichlet Tessellation Regions -- 7.1 Known Mesh Seed or Generating Points -- 7.2 Julia Set Image Example -- 7.3 Strongly Near Regions and Mesh Cells -- 7.4 Back to Earth -- References -- 8 Proximal Manifolds -- 8.1 Manifolds: Basic Notions -- 8.2 Charts and Atlases -- 8.3 Proximal Voronoï Manifolds, Atlases and Charts -- 8.4 Mean Shift Manifold -- 8.5 Digital Image Manifolds -- 8.6 Mean-Shift Image Manifolds -- 8.7 Image Saliency Manifolds -- 8.8 Selfie Voronoï Manifold -- 8.9 Manifolds with a Proximity -- References -- 9 Watershed, Smirnov Measure, Fuzzy Proximity and Sorted Near Sets -- 9.1 See-Through MM Segments Via Dirichlet Tessellation on an Image -- 9.2 Strongly Near Voronoï Region Interiors on MM Segmentations -- 9.3 Extension of Smirnov Proximity Measure -- 9.4 Fuzzy Lodato Proximity and Fuzzy Lodato--Smirnov Membership Function -- 9.5 Descriptive Smirnov Proximity -- 9.6 Application: Sorting Near Sets Using Smirnov Proximity Measures -- 9.7 Fuzzy Descriptive Lodato Proximity Space -- 9.8 Image Dilation -- 9.9 MorphologicalBinarize Operation with Lower and Upper Bounds -- 9.10 Dilation Method -- 9.11 Dilation and Watershed Segmentation -- 9.12 Gradient Filtering Watershed Components -- References -- 10 Strong Connectedness Revisited -- 10.1 Connectedness: Basic Concepts -- 10.2 Strongly Connected Subsets in a Voronoï Mesh -- References -- 11 Helly's Theorem and Strongly Proximal Helly Theorem -- 11.1 Helly's Theorem. , 11.2 Strongly Near Version of Helly's Theorem -- 11.3 Descriptive Helly's Theorem -- 11.4 Polyforms -- References -- 12 Nerves and Strongly Near Nerves -- 12.1 Polyform Nerves -- References -- 13 Connnectedness Patterns -- 13.1 Connectedness in Voronoï Meshes -- 13.2 Nearness of Collections of Strongly Connected Sets -- 13.3 Picture Mesh Patterns -- 13.4 Pattern Axioms and Object Signature Axioms -- 13.5 Keypoints Mesh Sites -- 13.6 Keypoints Mesh Patterns -- References -- 14 Nerve Patterns -- 14.1 Voronoï Mesh Nerves -- 14.2 Nerves with a Nucleus -- 14.3 Partial Ordering of Nuclei -- 14.4 Voronoï Mesh Nerve Patterns -- References -- Appendix AMathematica and Matlab Scripts -- Appendix BKuratowski Closure Axioms -- Appendix CSets. A Topological Perspective -- Appendix DBasics of Proximities -- Appendix ESet Theory Axioms, Operations and Symbols -- Appendix FTopology of Digital Images -- Author Index -- Subject Index.

Note: Intro -- Title Page -- Preface -- Organization -- Table of Contents -- Some Rough Consequence Logics and their Interrelations -- Introduction -- Two Variants of {\it S}5 -- The "Modus Ponens" (MP) Rules -- The Systems {\it Lr_{i}} -- Lr_1~ \sim~ Lr_5~ \sim~ Triv -- Lr_2~\sim ~Lr_{\sim\kern-2pt> -- }~\sim ~Lr_{\approx}~\sim ~S5(2)~\prec ~Lr_1 -- Lr_4~\prec~Lr_3~\sim~Lr_0~\sim~S5(1)~\prec~Lr_2} -- The Banerjee and Chakraborty Systems, Ja´skowski's \it {J} and the Systems \it {Lr_{i}} -- Some Extended Systems -- The + Systems -- Conclusions -- References -- Local and Global Approximations for Incomplete Data -- Introduction -- BasicNotions -- Incomplete Data Sets -- Blocks of Attribute-Value Pairs -- Definability -- Local Approximations -- Global Approximations -- Conclusions -- References -- A Rough Set Approach to Multiple Criteria ABC Analysis -- Introduction -- Multiple Criteria Decision Analysis -- A Rough Set Approach to MCABC -- A Dominance-Based Rough Set Theory for MCABC -- Decision Rules for MCABC -- Application -- Background -- Decision Rule Generation Comparison -- Comparison of Classification Results -- Conclusions -- References -- Partially Ordered Monads and Rough Sets -- Introduction -- Monads and Submonads -- Examples of Monads -- The Powerset Monad -- Powerset Monads with Fuzzy Level Sets -- The Covariant Double Contravariant Powerset Monad -- The Fuzzy Filter Monad -- Basic Triples and Partially Ordered Monads -- Examples of Partially Ordered Monads -- The Crisp Powerset Monad -- The Fuzzy Powerset Monad -- Powerset Monads with Fuzzy Level Sets -- The Covariant Double Contravariant Powerset Monad and the Partially Ordered Fuzzy Filter Monad -- Previous Work on Partially Ordered Monads for Fuzzy Convergence -- Extension Structures -- \it {\Phi}-Cauchy Structures and Completions. , Compactness as Completeness and Monadic Compactifications -- Applications to Rough Sets -- Relations, Fuzzy Relations and Kleisli Categories -- Ordinary Relations and Rough Sets -- Inverse Relations -- Monadic Relations and Rough Monads -- Conclusions -- References -- A Rough Sets Approach to the Identification and Analysis of Factors Affecting Biological Control of Leafy Spurge -- Introduction -- The Rough Set Approach -- Approximation Space -- Rough Approximations -- Information Tables -- Dependency Analysis and Data Reduction -- Computation of Rules -- Experiments -- Experimental Procedure -- Data Collection and Usage -- Results and Analysis -- Data Modelling and Analysis -- Release Factors -- Physical Factors -- Ecological Factors -- Vegetation Factors -- Combined Factors -- Conclusion -- References -- Interpretation of Extended Pawlak Flow Graphs Using Granular Computing -- Introduction -- Related Work -- Flow Graphs and Its Extension -- Flow Graph -- An Extension of Flow Graph -- Relationship Between EFG and GrC -- Granulation -- Decomposition and Composition of Granules -- Inference and Reformation -- Reduction of EFG -- Reformation Method -- Inference Method -- Simulation Experiments -- Conclusion -- References -- Generalized Indiscernibility Relations: Applications for Missing Values and Analysis of Structural Objects -- Introduction -- Knowledge Representation -- Reality Perceived by Sensors -- Semantics of Knowledge -- Language -- Information Systems -- Complete Data -- Incomplete Data -- Multivalued Attributes -- Structural Objects -- Sequential Data Processing -- Syntactic Rules -- Data Sequence Representation -- Parser Algorithm -- Semantic Values of Grammar Symbols -- Semantic Attachments -- Set Approximations -- Conclusions -- References -- A Categorical Approach to Mereology and Its Application to Modelling Software Components. , Introduction -- Standard Mereology -- Elements of Category Theory -- Introduction to Mereocat -- Mereocat Sums -- Independent Sum -- Interactive Sum -- Generalised Sum -- Mereocat Product -- Categorical Connector Framework -- Software Components and Mereocat -- Conclusion -- References -- Esoteric Rough Set Theory: Algebraic Semantics of a Generalized VPRS and VPFRS -- Introduction -- Generalized Covers Approach -- Concrete Katrinak Algebras -- Esoteric Rough Set Theory -- Exceptional Sets -- Equalities in Esoteric Rough Set Theory -- Connections with Equalities in the Rough Context and Dynamic Extensions -- Generalized Esoteric Covers -- Three Algebraic Semantics -- Examples -- Esoteric Rough Set Theory, VPRS and VPRFS -- Relativised Approximations -- Conclusion -- References -- Domain Knowledge Assimilation by Learning Complex Concepts -- Introduction -- Knowledge Elicitation from External Expert -- Ontology Matching -- Analysis of Outlier Cases -- Implementation -- Conclusion -- References -- Information Quanta and Approximation Operators: Once More Around the Track -- Introduction -- Information Structures and Approximation Operators -- Approximation Operators, Heyting-Brouwer Algebras and Rough Sets -- Concluding Remarks -- References -- On Partial Covers, Reducts and Decision Rules -- Introduction -- Partial Covers -- Main Notions -- Known Results -- On Polynomial Approximate Algorithms -- Bounds on C_{min}(\alpha) Based on Information About Greedy Algorithm Work -- Upper Bound on C_{greedy}(\alpha) -- On Covers for the Most Part of Set Cover Problems -- Partial Tests and Reducts -- Main Notions -- Relationships between Partial Covers and Partial Tests -- On Precision of Greedy Algorithm -- On Polynomial Approximate Algorithms -- Bounds on R_{min}(\alpha) Based on Information About Greedy Algorithm Work. , Upper Bound on R_{greedy}(\alpha) -- On Tests for the Most Part of Binary Decision Tables -- Partial Decision Rules -- Main Notions -- Relationships between Partial Covers and Partial Decision Rules -- On Precision of Greedy Algorithm -- On Polynomial Approximate Algorithms -- Bounds on L_{min}(\alpha) Based on Information About Greedy Algorithm Work -- Upper Bound on L_{greedy}(\alpha) -- On Decision Rules for the Most Part of Binary Decision Tables -- Conclusions -- References -- Evolutionary Rough k-Medoid Clustering -- Introduction -- Rough k-Means Algorithms -- Basic Properties of Rough Sets -- Lingras' Rough k-Means Cluster Algorithm -- Mitra's Evolutionary Extension of the Rough k-Means -- Classic k-Medoid Clustering -- The Algorithm -- Comparison of k-Medoids and k-Means -- Evolutionary Rough k-Medoids -- Rough k-Medoids Algorithms -- Objective Functions -- An Evolutionary Extension of the Rough k-Medoids -- Experiments -- Synthetic Data -- Colon Cancer Data -- Forest Data -- Control Chart Data -- Conclusion -- References -- The Rough Set Database System -- Introduction -- Capabilities of the System -- Home Page -- Adding Data - Online -- Searching for Data -- Editing the Existing Data -- The Classification of Publications with the Use of a Defined Classificator -- Registration of Users into the System -- Saving Data in a File -- Sending Files with Data to an Administrator -- Handling the Users Comments -- Statistics -- Help -- FAQ -- Software -- People -- Opinions -- Interactive Map of the World -- Plans for the Future -- Conclusions -- References -- A Model of User-Oriented Reduct Construction for Machine Learning -- Introduction -- User Preference of Attributes -- Quantitative Judgement of Attributes -- Qualitative Judgement of Attributes -- Connections between Quantitative and Qualitative Judgements of Attributes. , User Preference of Attribute Sets -- Basic Properties -- Quantitative Judgement of Attribute Sets -- Qualitative Judgement of Attribute Sets -- User Preference of Reducts -- Preliminaries -- The Deletion Algorithm -- The Addition Algorithm -- Conditional User Preferences -- Conditional User Preference of Attributes -- Reduct Construction Based on Conditional Preferences -- Conclusion -- References -- Research on Rough Set Theory and Applications in China -- Introduction -- Development of the Chinese Rough Set and SoftComputing Society -- Organization of CRSSC -- Key Research Groups of CRSSC -- General Status of Research on Rough Set Theory and Applications in China -- Research on Rough Set Theory and Its Applications in China -- Fundamentals of Rough Sets -- Knowledge Acquisition -- Granular Computing Based on Rough Sets -- Extended Rough Set Models -- Rough Logic -- Applications of Rough Sets -- Summary -- References -- Rough Neural Fault Classification of Power System Signals -- Introduction -- Power System Fundamentals -- Power Systems -- Power System Faults -- Mathematics Underlying Fault Classification and Recognition Techniques -- Rough Set Theory -- Classifier Fusion Theory -- Technology Review of Power System Fault Classification (PSFC) -- Wavelet Applications in Power Systems -- Combination of the Wavelet and Neural Network Techniques for Fault Detection -- Time-Frequency Representation Technique for Classifying Power Quality Disturbances -- Data Preparation for Manitoba Hydro HVDC PSFC -- Data Conversion -- Signal Grouping -- Signal Preprocessing and Feature Extraction for PSFC -- Signal Characteristics in Normal Condition -- Feature Extraction of 12 Types of Faults -- Rough Membership Neural Network (rmNN) for PSFC -- Sample Information System For PSFC -- Rough Membership Functions. , Rough Membership Tables for rmNN Training and Verification.

Note: Intro -- Preface -- Organization -- Table of Contents -- Three-Valued Logics, Uncertainty Management and Rough Sets -- 1 Introduction -- 2 Aggregation Functions on Three Valued Logics -- 2.1 Connectives -- 2.2 Logical Systems -- 2.3 Connections among Logics -- 2.4 Connectives on Nested Pairs and Orthopairs of Sets -- 3 Three-Valued Connectives on Ill-Known Sets -- 4 Three-Valued Connectives on Rough Sets -- 4.1 Some Basics of Rough Sets -- 4.2 Rough Sets and External Truth-Functionality -- 4.3 The Interpretability of External Truth-Functional Operations -- 5 Rough Sets: From Modal Logic to Three-Valued Logics -- 5.1 The Standard Modal Approach to Rough Sets -- 5.2 The Three-Valued Modal Approach -- 5.3 From Three-Valued Rough Set Logic to Modal Logic -- 6 Conclusion -- References -- Standard Errors of Indices in Rough Set Data Analysis -- 1 Introduction -- 2 Statistical Notation and Preliminaries -- 3 Simple Precision and the Approximation Quality -- 3.1 Approximation Quality and Accuracy -- 3.2 Standard Error of One Index -- 4 Two Sample Comparisons -- 5 Comparing Categories -- 5.1 Comparing pi -- 5.2 Comparing αi -- 5.3 Comparing pi-Values -- 6 Discussion -- References -- Proximity System: A Description-Based System for Quantifying the Nearness or Apartness of Visual Rough Sets -- 1 Introduction -- 2 Visual Rough Sets -- Overview of Rough Sets: -- 3 Description-Based Set Operators -- 4 Metric-Free Nearness Measure -- 5 Proximity System -- 6 Proximity System: Visual Rough Set Examples -- 7 Application: Human Visual Search -- 8 Conclusion -- References -- Rough Sets and Matroids -- 1 Introduction -- 2 Preliminaries -- 2.1 Rough Sets -- 2.2 Matroids -- 3 Matroids Generated by Approximation Spaces -- 4 Properties of Parameterized Matroids of Approximation Spaces, and Their Characterization -- 5 Conclusions -- References. , An Efficient Approach for Fuzzy Decision Reduct Computation -- 1 Introduction -- 2 Overview of Fuzzy Decision Reduct -- 2.1 Fuzzy Rough Set Theory -- 2.2 Modified Quick Reduct Algorithm -- 3 Improvements to Modified Quick Reduct Algorithm -- 3.1 Theoritical Foundations -- 3.2 Improved Modified Quick Reduct Algorithm (IMQRA) -- 3.3 Modeling of IMQRA Computations Using Vector Operations -- 3.4 Analysis of IMQRA Algorithm -- 4 Illustration -- 4.1 Positive Region Computation Using Conventional Approaches -- 4.2 Positive Region Computation Using Vector Operations -- 4.3 Illustration of IMQRA_MW Algorithm -- 5 Experiments and Results -- 5.1 Experiments with IMQRA_MW Algorithm -- 6 Analysis of Results -- 7 Conclusion -- References -- Rough Sets in Economy and Finance -- 1 Introduction -- 2 Rough Sets Overview -- 2.1 Information and Decision Systems -- 2.2 Indiscernibility Relation -- 2.3 Set Approximation and Boundaries -- 2.4 Attribute Dependency in Decision Systems -- 2.5 Reducts and Discernibility Matrix -- 2.6 Extensions of Rough Set Theory -- 3 Application of Rough Sets in Economy and Finance -- 3.1 Risk Management -- 3.2 Financial Time Series Forecasting and Trading Rules -- 3.3 Active Portfolio Management and Asset Valuation -- 4 Conclusion and Future Research Areas -- References -- Algorithms for Similarity Relation Learning from High Dimensional Data -- 1 Introduction -- 1.1 Motivation and Aims -- 1.2 Main Contributions -- 1.3 Plan of the Dissertation -- 2 Theory of Rough Sets -- 2.1 Introduction to Rough Sets -- 2.2 Rough Set Approximations -- 2.3 Attribute Reduction -- 3 Notion of Similarity -- 3.1 Similarity as a Relation -- 3.2 Similarity in a Context -- 3.3 Similarity Function and Classification Rules -- 3.4 Commonly Used Similarity Models -- 3.5 Similarity in Machine Learning -- 4 Similarity Relation Learning Methods -- 4.1 Problem Statement. , 4.2 Examples of Similarity Learning Models -- 5 Rule-Based Similarity Learning Model -- 5.1 General Motivation for Rule-Based Similarity -- 5.2 Construction of the Rule-Based Similarity Model -- 5.3 Properties of the Rule-Based Similarity Function -- 5.4 Rule-Based Similarity for High Dimensional Data -- 5.5 Unsupervised Rule-Based Similarity for Textual Data -- 5.6 Summary of the Rule-Based Similarity Models -- 6 Experimental Evaluation of the Rule-Based Similarity Model -- 6.1 Performance of Rule-Based Similarity in a Classification Context -- 6.2 Evaluation of the Dynamic Rule-Based Similarity Model on Microarray Data -- 6.3 Unsupervised Similarity Learning from Textual Data -- 7 Concluding Remarks -- 7.1 Summary -- 7.2 Future Works -- References -- Author Index.

Note: Intro -- Preface -- Table of Contents -- Author Index.

Note: Intro -- Preface -- LNCS Transactions on Rough Sets -- Table of Contents -- Author Index.

Note: Intro -- Preface -- LNCS Transactions on Rough Sets -- Contents -- Jan Łukasiewicz Life, Work, Legacy -- 1 Introduction -- 2 The Milieu -- 3 Years of Jan Łukasiewicz to 1939, the Outbreak of War -- 4 Years of War and Emigration -- 5 Epilogue -- 6 Comments -- References -- Descriptive Topological Spaces for Performing Visual Search -- 1 Introduction -- 2 Background -- 2.1 Visual Search Psychological Model -- 2.2 Near Sets -- 3 Preliminaries -- 3.1 Perceptual System -- 3.2 Descriptive Topologies -- 3.3 Descriptive Proximities -- 3.4 Descriptive Patterns -- 3.5 Tolerance-Based Descriptive Intersection Operator -- 4 Descriptive Visual Search System -- 4.1 Bottom-Up Attention -- 4.2 Convolutional Neural Network-Based Probe Functions -- 4.3 Top-Down Attention -- 5 Results and Discussion -- 5.1 Experimental Setup -- 5.2 ImageNet Results -- 5.3 SIMPLIcity Results -- 6 Conclusion -- References -- Double Successive Rough Set Approximations -- 1 Successive Approximations -- 2 Basic Concepts of Rough Set Theory -- 2.1 Properties Satisfied by Rough Sets -- 2.2 Dependencies in Knowledge Bases -- 3 Properties of Successive Approximations -- 4 Decomposing L2L1 Approximations -- 4.1 Characterising Unique Solutions -- 4.2 A Derived Preclusive Relation and a Notion of Independence -- 4.3 Seeing One Equivalence Relation Through Another -- 5 Decomposing U2U1 Approximations -- 5.1 Characterising Unique Solutions -- 6 Decomposing U2L1 Approximations -- 6.1 Characterising Unique Solutions -- 7 Decomposing L2U1 Approximations -- 7.1 Characterising Unique Solutions -- 8 Conclusion -- References -- Dialectical Rough Sets, Parthood and Figures of Opposition-I -- 1 Introduction -- 1.1 Background -- 2 Types of Preprocessing and Ontology -- 2.1 Granular Operator Spaces and Property Systems -- 3 Dialectical Negation -- 3.1 Dialectical Contradiction and Contradiction. , 3.2 Dialectical Predication -- 4 Dialectical Rough Sets -- 4.1 Enriched Classical Rough Set Theory -- 4.2 Dialectical Rough Logic -- 4.3 Parthoods -- 5 General Parthood -- 6 Figures of Dialectical Opposition -- 6.1 Classical Case-1: Fixed Truth -- 6.2 Case-2: Pseudo Gluts -- 6.3 Counting Procedures and Dialectical Opposition -- References -- A Logic for Spatial Reasoning in the Framework of Rough Mereology -- 1 Introduction -- 1.1 Mereology Based on the Notion of a Part -- 1.2 Mereology Based on Connection -- 1.3 The Model ROM for Connection Based Mereology -- 1.4 Rough Mereology -- 2 The Mass-Based Rough Mereology. Masses on a Mereological Universe -- 2.1 Mass-Based Logic (mRM-Logic) -- 3 Rough Inclusions in Mass-Based Mereological Universe -- 3.1 The Bayes Theorem in Mass-Based Rough Mereology -- 4 Spatial Reasoning in Mass Based Mereology: Betweenness -- 5 Spatial Reasoning in Mass Based Mereology: The Environments of Regular Open and Regular Closed Sets -- 6 Spatial Reasoning in Mass Based Mereology: Mereological Potential Fields -- 7 Spatial Reasoning in Mass Based Mereology: Planning for Teams of Robots -- 8 Spatial Reasoning on the Boolean Algebra of Regular Open/Closed Sets with a Mass Assignment: Potential Issues -- 9 Appendix: Topological Context of Spatial Reasoning -- 9.1 An Application: The Model ROM for Connection -- References -- Compound Objects Comparators in Application to Similarity Detection and Object Recognition -- 1 Introduction -- 1.1 Plan of the Dissertation -- 1.2 Research Problem. Thesis and Objectives of the Dissertation -- 2 Introductory Information -- 2.1 Fuzzy Sets -- 2.2 Selected Models of Uncertain Information -- 2.3 Similarity Issues -- 2.4 Object Identification Issues -- 2.5 Selected Aspects of Learning in Respect of Decision Models -- 2.6 Selected Aspects of Information Synthesis -- 3 Comparators. , 3.1 Introductory Information -- 3.2 Definitions of Comparator Components -- 3.3 Comparator Architecture -- 3.4 Granular Structures -- 3.5 Required Comparator Properties -- 3.6 Comparator Fuzzy Interpretation -- 3.7 Example -- 3.8 Automatic Correction of Results -- 3.9 Selected Issues of Comparators' Learning -- 3.10 Selected Extensions of Comparators -- 3.11 Summary -- 4 Comparator Networks -- 4.1 Introductory Information -- 4.2 Definitions of Components of Comparator Networks -- 4.3 Translator -- 4.4 Designing Comparator Networks -- 4.5 Types of Networks -- 4.6 Heterogeneous Network -- 4.7 Granular Processing of Information in Networks -- 4.8 Aggregation of Partial Results -- 4.9 Example -- 4.10 Fuzzy Interpretation of Heterogeneous Networks -- 4.11 Selected Issues of Learning of Comparators Network -- 4.12 Learning Issues of the Reference Set for Homogeneous Networks -- 4.13 Summary -- 5 Selected Applications of Comparator Networks -- 5.1 Methodology of Conduct -- 5.2 Overview of Applications -- 5.3 Identification of Contour Maps -- 5.4 Classification of References in Scientific Publications -- 5.5 Risk Recognition for Fire and Rescue Actions -- 6 Summary -- References -- Rseslib 3: Library of Rough Set and Machine Learning Methods with Extensible Architecture -- 1 Introduction -- 2 Related Work -- 3 Data -- 4 Discretizations -- 4.1 Equal Width -- 4.2 Equal Frequency -- 4.3 One Rule -- 4.4 Static Entropy Minimization -- 4.5 Dynamic Entropy Minimization -- 4.6 ChiMerge -- 4.7 Global Maximal Discernibility Heuristic -- 4.8 Local Maximal Discernibility Heuristic -- 5 Discernibility Matrix -- 6 Reducts -- 7 Rules Generated from Reducts -- 8 Classification -- 8.1 Rough Set Classifier -- 8.2 K Nearest Neighbors/RIONA -- 8.3 K Nearest Neighbors with Local Metric Induction -- 8.4 Classical Classifiers -- 9 Other Algorithms. , 10 Extensible Modular Component-Based Architecture -- 11 Tools -- 11.1 Rseslib Classifiers in Weka -- 11.2 Graphical Interface Qmak -- 11.3 Computing in Cluster -- 12 Rseslib Usage Examples -- 13 Conclusions and Future Work -- References -- Author Index.

Note: Intro -- Title Page -- Preface -- Organization -- Table of Contents -- Rough Set Theory: Ontological Systems, Entailment Relations and Approximation Operators -- Introduction -- Ontological Information Systems -- Information Quanta and Approximation Operators -- Rough Set Theory -- Logical Information Systems -- Summary -- References -- Information Entropy and Granulation Co-Entropy of Partitions and Coverings: A Summary -- Introduction -- Entropy of Abstract Discrete Probability Distributions -- Partitions -- The Information System Approach to Rough Set Theory by Partitions -- The Partition Approach to Rough Set Theory -- Measures and Partitions -- Entropy (As Measure of Average Uncertainty) and Co-Entropy (As Measure of Average Granularity) of Partitions -- Ordering on Partitions -- Isotonic Behavior of Entropies and Co-Entropies of Partitions -- A Pointwise Approach to the Entropy and Co-Entropy of Partitions -- Local Rough Granularity Measure in the Case of Partitions -- Application to Complete Information Systems: The Case of Fixed Universe -- Application to Complete Information Systems: The Case of Fixed Attributes -- Partial Partitions -- Local Rough Granularity Measure in the Case of Partial Partitions -- Coverings -- Genuine Coverings -- Orderings and Quasi-Orderings on Coverings -- Entropies and Co-Entropies of Coverings: The "Global" Approach -- Pointwise Approaches to the Entropy and Co-Entropy of Coverings -- Conclusions -- References -- Lattices with Interior and Closure Operators and Abstract Approximation Spaces -- Introduction -- Abstract Approximation Spaces -- The Partition Approach to Rough Set Theory -- Partition Approximation Spaces from Information Systems -- Lower and Upper Approximation Spaces: Their Duality in the Context of de Morgan Lattices. , Some Concrete Models: Partition, Topological, and Covering Approximation Spaces -- Partition Approximation Spaces Revisited -- Topological Approximation Spaces -- Covering Approximation Spaces -- The Tarski Closure and Interior Abstract Approach to Approximation Spaces -- The Lattice-Algebraic Semantic of S4-Like Modal Logic Induced by Tarski Closure -- A Comparison among the Algebraic-Semantic Tarski Closure Lattice, the Kripke Semantic Standard Model and the Syntactic Normal Systems of Modal Logic -- The Tarski Closure Induced from an Incomplete Information System -- The Similarity Kripke and the Preclusive Galois Connection Models: A Comparison -- Conclusions -- References -- Rough Approximation Based on Weak q-RIFs -- Introduction -- Preliminaries -- RIFs, q-RIFs, and Weak q-RIFs -- Rough Approximation Spaces Generalized -- Properties of Approximation Operators -- Approximation of Sets by Means of Operators Based on Special Weak q-RIFs -- FinalRemarks -- References -- Rough Geometry and Its Applications in Character Recognition -- Introduction -- Rough Geometry -- Rough Sets -- Rough Space and Rough Configuration -- Geometric Invariants of Upper Approximation Transformation -- Problems and Possible Improvement -- Application of Rough Geometry -- Application in Equichordal Point Problem -- Application in Principal Curves -- Conclusion and Prospect -- References -- Extensions of Information Systems: The Rough Set Perspective -- Introduction -- Rough Set Rudiments -- Information Systems -- Approximation of Sets -- Decision Language and Rules -- Consistent and Partially Consistent Extensions of Information Systems -- Rough Set Approach to Computing Extensions -- Concluding Remarks -- References -- Intangible Assets in a Polish Telecommunication Sector - Rough Sets Approach -- Introduction -- Intangible Assets -- Basic Concept of Rough Sets. , Concept 1: The Rough Sets Theory and Indiscernibility of Objects -- Concept 2: Information System -- Concept 3: Approximation of Sets -- Concept 4: Accuracy and Quality of Approximation -- Concept 5: Dependency of Attributes -- Concept 6: Significance of Attributes -- Concept 7: Attribute Reduction -- Application of Rough Sets -- Research - Goals and Assumptions -- Methodology and Data -- Results -- Conclusions -- References -- Multicriteria Attractiveness Evaluation of Decision and Association Rules -- Introduction -- Knowledge Discovery -- Attractiveness Measures and Their Properties -- Aim and Scope of the Article -- Basic Quantitative Rule Description -- Attractiveness Measures for Decision and Association Rules -- Desirable Properties of Attractiveness Measures -- Analyses of Properties of Particular Attractiveness Measures -- Analysis of Measures with Respect to Property M -- Analysis of Measures with Respect to Property of Confirmation -- Analysis of Measures with Respect to Property of Hypothesis Symmetry -- Multicriteria Attractiveness Evaluation of Rules -- Definitions of Orders and Pareto-optimal Set -- Support-Confidence Evaluation Space -- Support-f Evaluation Space -- Support-s Evaluation Space -- Support and Confirmation Measures with the Property M Evaluation Space -- Support-anti-support Evaluation Space -- Confirmation Perspective on Support-anti-support Evaluation Space -- Examples of Application of Attractiveness Measures to Multicriteria Rule Evaluation -- Multicriteria Rule Evaluation System -- Examples of the System's Application -- Conclusions -- References -- Author Index.

Note: Title Page -- Preface -- Table of Contents -- Mining Numerical Data - A Rough Set Approach -- Introduction -- Discretization Methods -- MLEM2 -- Numerical and Incomplete Data -- Experiments -- Conclusions -- References -- Definability and Other Properties of Approximations for Generalized Indiscernibility Relations -- Introduction -- Basic Definitions -- Set Approximations in the Pawlak Space -- Subset, Singleton and Concept Approximations -- Modified Singleton Approximations -- Largest Lower and Smallest Upper Approximations -- Dual Approximations -- Approximations with Mixed Idempotency -- Coalescence of Rough Approximations -- Conclusions -- References -- Variable Consistency Bagging Ensembles -- Introduction -- Consistency Sampling Algorithms -- Bagging Scheme -- Variable Consistency Sampling -- Consistency Measures -- Experimental Setup for Variable Consistency Bagging with Rules and Trees Base Classifiers -- Results of Experiments -- Conclusions -- References -- Classical and Dominance-Based Rough Sets in the Search for Genes under Balancing Selection -- Introduction -- Genetic Data -- Methodology -- Results and Discussion -- Conclusion -- References -- Satisfiability Judgement under Incomplete Information -- Introduction -- Pawlak Information Systems: Descriptor Languages -- Approximation Spaces -- Granulation of the Universe -- Rough Inclusion -- Approximation of Concepts -- Mathematical Models of Satisfiability -- The Relational Model -- The Logical Value-Based Model -- The Extension-Based Model -- Three Research Problems Concerning Satisfiability -- A More Realistic Scenario -- Actors and Their Roles -- Information Available to System S -- Languages for Specifying Properties and Representing Knowledge -- From Infosystems to Approximation Spaces -- Learning of Satisfiability vs. Concept Approximation -- The Importance of Domain Knowledge. , Problems with Learning of the Notion of Satisfiability -- Discovery of Satisfiability Judgement -- Rough Satisfiability Relations -- Case-Based Satisfiability Judgement -- Summary -- References -- Irreducible Descriptive Sets of Attributes for Information Systems -- Introduction -- Maximal Consistent Extensions -- On Membership to Ext(S) -- Separating Sets of Attributes -- On Construction of C(Ext(S)) -- Descriptive Sets of Attributes -- On Cardinality of Irreducible Descriptive Sets -- Descriptions of Ext(S) and Rul(S) -- Conclusions -- References -- Computational Theory Perception (CTP), Rough-Fuzzy Uncertainty Analysis and Mining in Bioinformatics and Web Intelligence: A Unified Framework -- Introduction -- Computational Theory of Perceptions and F-Granulation -- Granular Computation and Rough-Fuzzy Approach -- Rough-Fuzzy Granulation and Case Based Reasoning -- Rough-Fuzzy Clustering -- Quantitative Measures -- Rough Fuzzy C-Medoids and Amino Acid Sequence Analysis -- Rough Ensemble Classifier for Web Services -- Conclusions -- References -- Decision Rule-Based Data Models Using TRS and NetTRS - Methods and Algorithms -- Introduction -- TRS Library Functionality -- Tolerance Thresholds -- Decision Rules -- Rules Generalization and Filtration -- Classification -- Rules Quality Measures -- Selected Results Obtained by Algorithms Included in the TRS Library -- Searching Tolerance Thresholds -- Rules Induction -- Rules Joining -- Rules Filtration -- TRS Results - Comparison with Other Methods and a Real-Life Data Analysis Example -- Conclusions -- References -- A Distributed Decision Rules Calculation Using Apriori Algorithm -- Introduction -- Computing Rules and Rough Sets Basis -- Apriori Algorithm -- Tree Structure for Keeping Candidate Rules -- Recursive Version of Apriori -- Parallel Computations -- The Problem of Redundancy of Partial Results. , Optimal Usage of Processors -- Results of Experiments -- Conclusions and Future Work -- References -- Decision Table Reduction in KDD: Fuzzy Rough Based Approach -- Introduction -- Review of Fuzzy Rough Sets -- Decision Table Reduction with Fuzzy Rough Sets -- Attribute-Value Reduction -- Rule Covering System -- An Illustrative Example -- Conclusion -- References -- Author Index.

Note: Title Page -- Preface -- Organizations -- Table of Contents -- Dynamic Rule-Based Similarity Modelfor DNA Microarray Data -- Introduction -- Preliminaries -- Similarity and Its Properties -- Motivations for Rule-Based Similarity -- Dynamic Rules-Based Similarity Model -- Performance of the Dynamic Rules-Based Similarity Model -- Conclusions and Directions for the Future -- References -- Multi-valued Approach to Near Set Theory -- Introduction -- Basic Concepts -- Multi-valued System for Near Set Theory -- New Approaches to Near Sets -- Conclusion -- References -- Perceptual Indiscernibility, Rough Sets, Descriptively Near Sets, and Image Analysis -- Introduction -- Related Works -- Preliminaries: Rough Sets and Perceptual Nearness of Sets -- Visual Rough Sets -- Tolerance Rough Sets -- Nearness of Sets -- Near Sets -- Perceptual Tolerance Relation -- Tolerance Near Sets -- Nearness Measure -- Finding Classes -- Digital Image Features -- Normalized RGB -- Entropy -- Mean Shift Segmentation Algorithm -- Multiscale Edge Detection -- Grey Level Co-occurrence Matrices -- Zernike Moments -- CIELUV Colour Space -- Application of Near Sets -- Perceptual Image Analysis -- Initial Results -- Parameter Adjustment -- Other Measures -- SIMPLIcity Image Database -- Discussion -- Future Work -- Conclusion -- References -- Dialectics of Counting and the Mathematics of Vagueness -- Introduction -- Some Background, Terminology -- Semantic Domains, Meta and Object Levels -- Granules and Concepts -- Contamination Problem -- Formalism Compatibility and Mereology -- Motivating Examples for RYS -- Objectivity of Measures and General RST -- Numbers and Their Generalization -- Granules: An Axiomatic Approach -- Concepts of Discernibility -- Relative- and Multi-granulation -- Relation-Based Rough Set Theory -- Tolerance Spaces -- Cover-Based Rough Set Theory. , Classification of Rough Set Theory -- Dialectical Counting, Measures -- Generalized Measures -- Rough Inclusion Functions -- On Representation of Counts -- Representation of IPC -- Semantics from Dialectical Counting -- Rough Entanglement: Granular HPC -- Connections between Fuzzy and Rough Sets -- Operations on Low-Level Rough Naturals -- Further Directions: Conclusion -- References -- Author Index.