| Bayes' Theorem - the Rough Set Perspective | p. 1 |
| Introduction | p. 1 |
| Bayes' Theorem | p. 2 |
| Information Systems and Approximation of Sets | p. 2 |
| Decision Language | p. 4 |
| Decision Algorithms | p. 5 |
| Decision Rules in Information Systems | p. 6 |
| Properties of Decision Rules | p. 7 |
| Decision Tables and Flow Graphs | p. 8 |
| Illustrative Example | p. 8 |
| Conclusion | p. 11 |
| References | p. 12 |
| Approximation Spaces in Rough Neurocomputing | p. 13 |
| Introduction | p. 13 |
| Approximation Spaces in Rough Set Theory | p. 14 |
| Generalizations of Approximation Spaces | p. 15 |
| Information Granule Systems and Approximation Spaces | p. 16 |
| Classifiers as Information Granules | p. 18 |
| Approximation Spaces for Information Granules | p. 19 |
| Approximation Spaces in Rough-Neuro Computing | p. 20 |
| Conclusion | p. 21 |
| References | p. 22 |
| Soft Computing Pattern Recognition: Principles, Integrations and Data Mining | p. 23 |
| Introduction | p. 23 |
| Relevance of Fuzzy Set Theory in Pattern Recognition | p. 25 |
| Relevance of Neural Network Approaches | p. 27 |
| Genetic Algorithms for Pattern Recognition | p. 28 |
| Integration and Hybrid Systems | p. 29 |
| Evolutionary Rough Fuzzy MLP | p. 30 |
| Data mining and knowledge discovery | p. 31 |
| References | p. 33 |
| Generalizations and New Theories | |
| Generalization of Rough Sets Using Weak Fuzzy Similarity Relations | p. 37 |
| Introduction | p. 37 |
| Weak Fuzzy Similarity Relations | p. 38 |
| Generalized Rough Set Approximations | p. 41 |
| Generalized Rough Membership Functions | p. 43 |
| An Illustrative Example | p. 44 |
| Conclusions | p. 46 |
| References | p. 46 |
| Two Directions toward Generalization of Rough Sets | p. 47 |
| Introduction | p. 47 |
| The Original Rough Sets | p. 48 |
| Distinction among Positive, Negative and Boundary Elements | p. 50 |
| Approximations by Means of Elementary Sets | p. 54 |
| Concluding Remarks | p. 56 |
| References | p. 56 |
| Two Generalizations of Multisets | p. 59 |
| Introduction | p. 59 |
| Preliminaries | p. 60 |
| Infinite Memberships | p. 62 |
| Generalization of Membership Sequence | p. 64 |
| Conclusion | p. 67 |
| References | p. 67 |
| Interval Probability and Its Properties | p. 69 |
| Introduction | p. 69 |
| Interval Probability Functions | p. 70 |
| Combination and Conditional Rules for IPF | p. 74 |
| Numerical Example of Bayes' Formula | p. 75 |
| Concluding Remarks | p. 77 |
| References | p. 77 |
| On Fractal Dimension in Information Systems | p. 79 |
| Introduction | p. 79 |
| Fractal Dimensions | p. 80 |
| Rough Sets and Topologies on Rough Sets | p. 81 |
| Fractals in Information Systems | p. 84 |
| References | p. 86 |
| A Remark on Granular Reasoning and Filtration | p. 89 |
| Introduction | p. 89 |
| Kripke Semantics and Filtration | p. 90 |
| Relative Filtration with Approximation | p. 92 |
| Relative Filtration and Granular Reasoning | p. 94 |
| Concluding Remarks | p. 96 |
| References | p. 96 |
| Towards Discovery of Relevant Patterns from Parameterized Schemes of Information Granule Construction | p. 97 |
| Introduction | p. 97 |
| Approximation Granules | p. 99 |
| Rough-Fuzzy Granules | p. 101 |
| Granule Decomposition | p. 103 |
| References | p. 106 |
| Approximate Markov Boundaries and Bayesian Networks: Rough Set Approach | p. 109 |
| Introduction | p. 109 |
| Data Based Probabilistic Models | p. 110 |
| Approximate Probabilistic Models | p. 115 |
| Conclusions | p. 120 |
| References | p. 120 |
| Data Mining and Rough Sets | |
| Mining High Order Decision Rules | p. 125 |
| Introduction | p. 125 |
| Motivations | p. 126 |
| Mining High Order Decision Rules | p. 128 |
| Mining Ordering Rules: an Illustrative Example | p. 131 |
| Conclusion | p. 134 |
| References | p. 134 |
| Association Rules from a Point of View of Conditional Logic | p. 137 |
| Introduction | p. 137 |
| Preliminaries | p. 137 |
| Association Rules and Conditional Logic | p. 141 |
| Association Rules and Graded Conditional Logic | p. 143 |
| Concluding Remarks | p. 145 |
| References | p. 145 |
| Association Rules with Additional Semantics Modeled by Binary Relations | p. 147 |
| Introduction | p. 147 |
| Databases with Additional Semantics | p. 148 |
| Re-formulating Data Mining | p. 150 |
| Mining Semantically | p. 151 |
| Semantic Association Rules | p. 152 |
| Conclusion | p. 153 |
| References | p. 155 |
| A Knowledge-Oriented Clustering Method Based on Indis-cernibility Degree of Objects | p. 157 |
| Introduction | p. 157 |
| Clustering Procedure | p. 158 |
| Experimental Results | p. 164 |
| Conclusions | p. 166 |
| References | p. 166 |
| Some Effective Procedures for Data Dependencies in Information Systems | p. 167 |
| Preliminary | p. 167 |
| Three Procedures for Dependencies | p. 168 |
| An Algorithm for Rule Extraction | p. 173 |
| Dependencies in Non-deterministic Information Systems | p. 173 |
| Concluding Remarks | p. 176 |
| References | p. 176 |
| Improving Rules Induced from Data Describing Self-Injurious Behaviors by Changing Truncation Cutoff and Strength | p. 177 |
| Introduction | p. 177 |
| Temporal Data | p. 178 |
| Rule Induction and Classification | p. 181 |
| Postprocessing of Rules | p. 182 |
| Experiments | p. 182 |
| Conclusions | p. 184 |
| References | p. 184 |
| The Variable Precision Rough Set Inductive Logic Programming Model and Future Test Cases in Web Usage Mining | p. 187 |
| Introduction | p. 187 |
| The VPRS model and future test cases | p. 188 |
| The VPRSILP model and future test cases | p. 189 |
| A simple-graph-VPRSILP-ESD system | p. 190 |
| VPRSILP and Web Usage Graphs | p. 191 |
| Experimental details | p. 191 |
| Conclusions | p. 195 |
| References | p. 195 |
| Rough Set and Genetic Programming | p. 197 |
| Introduction | p. 197 |
| Rough Set Theory | p. 198 |
| Genetic Rough Induction (GRI) | p. 199 |
| Experiments and Results | p. 202 |
| Conclusions | p. 206 |
| References | p. 207 |
| Conflict Analysis and Data Analysis | |
| Rough Set Approach to Conflict Analysis | p. 211 |
| Introduction | p. 211 |
| Conflict Model | p. 212 |
| System with Constraints | p. 216 |
| Analysis | p. 216 |
| Agents' Strategy Analysis | p. 218 |
| Conclusions | p. 220 |
| References | p. 220 |
| Criteria for Consensus Susceptibility in Conflicts Resolving | p. 223 |
| Introduction | p. 223 |
| Consensus Choice Problem | p. 224 |
| Susceptibility to Consensus | p. 226 |
| Conclusions | p. 232 |
| References | p. 232 |
| Li-Space Based Models for Clustering and Regression | p. 233 |
| Introduction | p. 233 |
| Fuzzy c-means Based on L1-space | p. 234 |
| Mixture Density Model Based on L1-space | p. 236 |
| Regression Models Based on Absolute Deviations | p. 237 |
| Numerical Examples | p. 239 |
| Conclusion | p. 239 |
| References | p. 240 |
| Upper and Lower Possibility Distributions with Rough Set Concepts | p. 243 |
| The Concept of Upper and Lower Possibility Distributions | p. 243 |
| Comparison of dual possibility distributions with dual approximations in rough set theory | p. 245 |
| Identification of Upper and Lower Possibility Distributions | p. 245 |
| Numerical Example | p. 248 |
| Conclusions | p. 250 |
| References | p. 250 |
| Efficiency Values Based on Decision Maker's Interval Pairwise Comparisons | p. 251 |
| Introduction | p. 251 |
| Interval AHP with Interval Comparison Matrix | p. 252 |
| Choice of the Optimistic Weights and Efficiency Value by DEA | p. 254 |
| Numerical Example | p. 257 |
| Concluding Remarks | p. 259 |
| References | p. 259 |
| Applications in Engineering | |
| Rough Measures, Rough Integrals and Sensor Fusion | p. 263 |
| Introduction | p. 263 |
| Classical Additive Set Functions | p. 264 |
| Basic Concepts of Rough Sets | p. 264 |
| Rough Measures | p. 265 |
| Rough Integrals | p. 265 |
| Multi-Sensor Fusion | p. 268 |
| Conclusion | p. 270 |
| References | p. 271 |
| A Design of Architecture for Rough Set Processor | p. 273 |
| Introduction | p. 273 |
| Outline of Rough Set Processor | p. 273 |
| Design of Architecture | p. 275 |
| Discussions | p. 279 |
| Conclusion | p. 280 |
| References | p. 280 |
| Identifying Adaptable Components - A Rough Sets Style Approach | p. 281 |
| Introduction | p. 281 |
| Defining Adaptation of Software Components | p. 281 |
| Identifying One-to-one Component Adaptation | p. 282 |
| Identifying One-to-many Component Adaptation | p. 288 |
| Conclusions | p. 289 |
| References | p. 290 |
| Analysis of Image Sequences for the UAV | p. 291 |
| Introduction | p. 291 |
| Basic Notions | p. 292 |
| The WITAS Project | p. 293 |
| Data Description | p. 294 |
| Tasks | p. 295 |
| Results | p. 296 |
| Conclusions | p. 299 |
| References | p. 300 |
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