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.- Two Directions toward Generalization of Rough Sets.- Two Generalizations of Multisets.- Interval Probability and Its Properties.- On Fractal Dimension in Information Systems.- A Remark on Granular Reasoning and Filtration.- Towards Discovery of Relevant Patterns from Parameterized Schemes of Information Granule Construction.- Approximate Markov Boundaries and Bayesian Networks: Rough Set Approach.- II. Data Mining and Rough Sets.- Mining High Order Decision Rules.- Association Rules from a Point of View of Conditional Logic.- Association Rules with Additional Semantics Modeled by BinaryRelations.- A Knowledge-Oriented Clustering Method Based on Indiscernibility Degree of Objects.- Some Effective Procedures for Data Dependencies in Information Systems.- Improving Rules Induced from Data Describing Self-Injurious Behaviors by Changing Truncation Cutoff and Strength.- The Variable Precision Rough Set Inductive Logic Programming Model and Future Test Cases in Web Usage Mining.- Rough Set and Genetic Programming.- III. Conflict Analysis and Data Analysis.- Rough Set Approach to Conflict Analysis.- Criteria for Consensus Susceptibility in Conflicts Resolving.- L1-Space Based Models for Clustering and Regression.- Upper and Lower Possibility Distributions with Rough Set Concepts.- Efficiency Values Based on Decision Maker’s Interval Pairwise Comparisons.- IV. Applications in Engineering.- Rough Measures, Rough Integrals and Sensor Fusion.- A Design of Architecture for Rough Set Processor.- Identifying Adaptable Components — A Rough Sets Style Approach.- Analysis of Image Sequences for the UAV.