Rough Set Theory and Granular Computing

After 20 years of pursuing rough set theory and its applications a look on its present state and further prospects is badly needed. The monograph Rough Set Theory and Granular Computing edited by Masahiro Inuiguchi, Shoji Hirano and Shusaku Tsumoto meets this demand. It presents the newest developments in this area and gives fair picture of the state of the art in this domain. Firstly, in the keynote papers by Zdzislaw Pawlak, Andrzej Skowron and Sankar K. Pal the relationship of rough sets with other important methods of data analysis -Bayes theorem, neuro computing and pattern recognitio- is thoroughly examined. Next, several interesting generalizations of the the­ ory and new directions of research are presented. Furthermore application of rough sets in data mining, in particular, rule induction methods based on rough set theory is presented and discussed. Further important issue dis­ cussed in the monograph is rough set based data analysis, including study of decisions making in conflict situations. Last but not least, some recent engi­ neering applications of rough set theory are given. They include a proposal of rough set processor architecture organization for fast implementation of ba­ sic rough set operations and discussion of results concerning advanced image processing for unmanned aerial vehicle. Thus the monograph beside presenting wide spectrum of ongoing research in this area also points out new emerging areas of study and applications, which makes it a valuable source of information to all interested in this do­ main.

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.