Rough Set Theory and Granular Computing

Bayes' Theorem - the Rough Set Perspective.- 1 Introduction.- 2 Bayes' Theorem.- 3 Information Systems and Approximation of Sets.- 4 Decision Language.- 5 Decision Algorithms.- 6 Decision Rules in Information Systems.- 7 Properties of Decision Rules.- 8 Decision Tables and Flow Graphs.- 9 Illustrative Example.- 10 Conclusion.- References.- Approximation Spaces in Rough Neurocomputing.- 1 Introduction.- 2 Approximation Spaces in Rough Set Theory.- 3 Generalizations of Approximation Spaces.- 4 Information Granule Systems and Approximation Spaces.- 5 Classifiers as Information Granules.- 6 Approximation Spaces for Information Granules.- 7 Approximation Spaces in Rough-Neuro Computing.- 8 Conclusion.- References.- Soft Computing Pattern Recognition: Principles, Integrations and Data Mining.- 1 Introduction.- 2 Relevance of Fuzzy Set Theory in Pattern Recognition.- 3 Relevance of Neural Network Approaches.- 4 Genetic Algorithms for Pattern Recognition.- 5 Integration and Hybrid Systems.- 6 Evolutionary Rough Fuzzy MLP.- 7 Data mining and knowledge discovery.- References.- I. Generalizations and New Theories.- Generalization of Rough Sets Using Weak Fuzzy Similarity Relations.- 1 Introduction.- 2 Weak Fuzzy Similarity Relations.- 3 Generalized Rough Set Approximations.- 4 Generalized Rough Membership Functions.- 5 An Illustrative Example.- 6 Conclusions.- References.- Two Directions toward Generalization of Rough Sets.- 1 Introduction.- 2 The Original Rough Sets.- 3 Distinction among Positive, Negative and Boundary Elements.- 4 Approximations by Means of Elementary Sets.- 5 Concluding Remarks.- References.- Two Generalizations of Multisets.- 1 Introduction.- 2 Preliminaries.- 3 Infinite Memberships.- 4 Generalization of Membership Sequence.- 5 Conclusion.- References.- Interval Probability and Its Properties.- 1 Introduction.- 2 Interval Probability Functions.- 3 Combination and Conditional Rules for IPF.- 4 Numerical Example of Bayes' Formula.- 5 Concluding Remarks.- References.- On Fractal Dimension in Information Systems.- 1 Introduction.- 2 Fractal Dimensions.- 3 Rough Sets and Topologies on Rough Sets.- 4 Fractals in Information Systems.- References.- A Remark on Granular Reasoning and Filtration.- 1 Introduction.- 2 Kripke Semantics and Filtration.- 3 Relative Filtration with Approximation.- 4 Relative Filtration and Granular Reasoning.- 5 Concluding Remarks.- References.- Towards Discovery of Relevant Patterns from Parameterized Schemes of Information Granule Construction.- 1 Introduction.- 2 Approximation Granules.- 3 Rough-Fuzzy Granules.- 4 Granule Decomposition.- References.- Approximate Markov Boundaries and Bayesian Networks: Rough Set Approach.- 1 Introduction.- 2 Data Based Probabilistic Models.- 3 Approximate Probabilistic Models.- 4 Conclusions.- References.- II. Data Mining and Rough Sets.- Mining High Order Decision Rules.- 1 Introduction.- 2 Motivations.- 3 Mining High Order Decision Rules.- 4 Mining Ordering Rules: an Illustrative Example.- 5 Conclusion.- References.- Association Rules from a Point of View of Conditional Logic.- 1 Introduction.- 2 Preliminaries.- 3 Association Rules and Conditional Logic.- 4 Association Rules and Graded Conditional Logic.- 5 Concluding Remarks.- References.- Association Rules with Additional Semantics Modeled by Binary Relations.- 1 Introduction.- 2 Databases with Additional Semantics.- 3 Re-formulating Data Mining.- 4 Mining Semantically.- 5 Semantic Association Rules.- 6 Conclusion.- References.- A Knowledge-Oriented Clustering Method Based on Indiscernibility Degree of Objects.- 1 Introduction.- 2 Clustering Procedure.- 3 Experimental Results.- 4 Conclusions.- References.- Some Effective Procedures for Data Dependencies in Information Systems.- 1 Preliminary.- 2 Three Procedures for Dependencies.- 3 An Algorithm for Rule Extraction.- 4 Dependencies in Non-deterministic Information Systems.- 5 Concluding Remarks.- References.- Improving Rules Induced from Data Describing Self-Injurious Behaviors by Changing Truncation Cutoff and Strength.- 1 Introduction.- 2 Temporal Data.- 3 Rule Induction and Classification.- 4 Postprocessing of Rules.- 5 Experiments.- 6 Conclusions.- References.- The Variable Precision Rough Set Inductive Logic Programming Model and Future Test Cases in Web Usage Mining.- 1 Introduction.- 2 The VPRS model and future test cases.- 3 The VPRSILP model and future test cases.- 4 A simple-graph-VPRSILP-ESD system.- 5 VPRSILP and Web Usage Graphs.- 6 Experimental details.- 7 Conclusions.- References.- Rough Set and Genetic Programming.- 1 Introduction.- 2 Rough Set Theory.- 3 Genetic Rough Induction (GRI).- 4 Experiments and Results.- 5 Conclusions.- References.- III. Conflict Analysis and Data Analysis.- Rough Set Approach to Conflict Analysis.- 1 Introduction.- 2 Conflict Model.- 3 System with Constraints.- 4 Analysis.- 5 Agents' Strategy Analysis.- 6 Conclusions.- References.- Criteria for Consensus Susceptibility in Conflicts Resolving.- 1 Introduction.- 2 Consensus Choice Problem.- 3 Susceptibility to Consensus.- 4 Conclusions.- References.- L1-Space Based Models for Clustering and Regression.- 1 Introduction.- 2 Fuzzy c-means Based on L1-space.- 3 Mixture Density Model Based on L1-space.- 4 Regression Models Based on Absolute Deviations.- 5 Numerical Examples.- 6 Conclusion.- References.- Upper and Lower Possibility Distributions with Rough Set Concepts.- 1 The Concept of Upper and Lower Possibility Distributions.- 2 Comparison of dual possibility distributions with dual approximations in rough set theory.- 3 Identification of Upper and Lower Possibility Distributions.- 4 Numerical Example.- 6 Conclusions.- References.- Efficiency Values Based on Decision Maker's Interval Pairwise Comparisons.- 1 Introduction.- 2 Interval AHP with Interval Comparison Matrix.- 3 Choice of the Optimistic Weights and Efficiency Value by DEA.- 4 Numerical Example.- 5 Concluding Remarks.- References.- IV. Applications in Engineering.- Rough Measures, Rough Integrals and Sensor Fusion.- 1 Introduction.- 2 Classical Additive Set Functions.- 3 Basic Concepts of Rough Sets.- 4 Rough Measures.- 5 Rough Integrals.- 6 Multi-Sensor Fusion.- 7 Conclusion.- References.- A Design of Architecture for Rough Set Processor.- 1 Introduction.- 2 Outline of Rough Set Processor.- 3 Design of Architecture.- 4 Discussions.- 6 Conclusion.- References.- Identifying Adaptable Components - A Rough Sets Style Approach.- 1 Introduction.- 2 Defining Adaptation of Software Components.- 3 Identifying One-to-one Component Adaptation.- 4 Identifying One-to-many Component Adaptation.- 5 Conclusions.- References.- Analysis of Image Sequences for the UAV.- 1 Introduction.- 2 Basic Notions.- 3 The WITAS Project.- 4 Data Description.- 5 Tasks.- 6 Results.- 7 Conclusions.- References.