Data Mining, Rough Sets and Granular Computing

During the past few years, data mining has grown rapidly in visibility and importance within information processing and decision analysis. This is par­ ticularly true in the realm of e-commerce, where data mining is moving from a "nice-to-have" to a "must-have" status. In a different though related context, a new computing methodology called granular computing is emerging as a powerful tool for the conception, analysis and design of information/intelligent systems. In essence, data mining deals with summarization of information which is resident in large data sets, while granular computing plays a key role in the summarization process by draw­ ing together points (objects) which are related through similarity, proximity or functionality. In this perspective, granular computing has a position of centrality in data mining. Another methodology which has high relevance to data mining and plays a central role in this volume is that of rough set theory. Basically, rough set theory may be viewed as a branch of granular computing. However, its applications to data mining have predated that of granular computing.

1: Granular Computing — A New Paradigm.- Some Reflections on Information Granulation and its Centrality in Granular Computing, Computing with Words, the Computational Theory of Perceptions and Precisiated Natural Language.- 2: Granular Computing in Data Mining.- Data Mining Using Granular Computing: Fast Algorithms for Finding Association Rules.- Knowledge Discovery with Words Using Cartesian Granule Features: An Analysis for Classification Problems.- Validation of Concept Representation with Rule Induction and Linguistic Variables.- Granular Computing Using Information Tables.- A Query-Driven Interesting Rule Discovery Using Association and Spanning Operations.- 3: Data Mining.- An Interactive Visualization System for Mining Association Rules.- Algorithms for Mining System Audit Data.- Scoring and Ranking the Data Using Association Rules.- Finding Unexpected Patterns in Data.- Discovery of Approximate Knowledge in Medical Databases Based on Rough Set Model.- 4: Granular Computing.- Observability and the Case of Probability.- Granulation and Granularity via Conceptual Structures: A Perspective From the Point of View of Fuzzy Concept Lattices.- Granular Computing with Closeness and Negligibility Relations.- Application of Granularity Computing to Confirm Compliance with Non-Proliferation Treaty.- Basic Issues of Computing with Granular Probabilities.- Multi-dimensional Aggregation of Fuzzy Numbers Through the Extension Principle.- On Optimal Fuzzy Information Granulation.- Ordinal Decision Making with a Notion of Acceptable: Denoted Ordinal Scales.- A Framework for Building Intelligent Information-Processing Systems Based on Granular Factor Space.- 5: Rough Sets and Granular Computing.- GRS: A Generalized Rough Sets Model.- Structure of Upper and Lower ApproximationSpaces of Infinite Sets.- Indexed Rough Approximations, A Polymodal System, and Generalized Possibility Measures.- Granularity, Multi-valued Logic, Bayes’ Theorem and Rough Sets.- The Generic Rough Set Inductive Logic Programming (gRS-ILP) Model.- Possibilistic Data Analysis and Its Similarity to Rough Sets.