Rough sets and boolean reasoning

In recent years we witness a rapid growth of interest in rough set theory and its applications, worldwide. The theory has been followed by the development of several software systems that implement rough set operations, in particular for solving knowledge discovery and data mining tasks. Rough sets are applied in domains, such as, for instance, medicine, finance, telecommunication, vibration analysis, conflict resolution, intelligent agents, pattern recognition, control theory, signal analysis, process industry, marketing, etc.We introduce basic notions and discuss methodologies for analyzing data and surveys some applications. In particular we present applications of rough set methods for feature selection, feature extraction, discovery of patterns and their applications for decomposition of large data tables as well as the relationship of rough sets with association rules. Boolean reasoning is crucial for all the discussed methods.We also present an overview of some extensions of the classical rough set approach. Among them is rough mereology developed as a tool for synthesis of objects satisfying a given specification in a satisfactory degree. Applications of rough mereology in such areas like granular computing, spatial reasoning and data mining in distributed environment are outlined.

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