Approximate Boolean Reasoning: Foundations and Applications in Data Mining

The rapidly growing volume and complexity of modern databases make the need for technologies to describe and summarize the information they contain increasingly important. Knowledge Discovery in Databases (KDD) and data mining are new research areas that try to overcome this problem. In [Fayyad et al., 1996], KDD was characterized as a non-trivial process of identifying valid, novel, potentially useful, and ultimately understandable patterns in data, while data mining is a process of extracting implicit, previously unknown and potentially useful patterns and relationships from data, and it is widely used in industry and business applications. As the main step in KDD, data mining methods are required to be not only accurate but also to deliver understandable and interpretable results for users, e.g., through visualization. The other important issue of data mining methods is their complexity and scalability. Presently, data mining is a collection of methods from various disciplines such as mathematics, statistics, logics, pattern recognition, machine learning, non-conventional models and heuristics for computing. Concept approximation problem is one of the most important issues in machine learning, knowledge discovery and data mining. Classification, clustering, association analysis or regression are examples of well known problems in data mining that can be formulated as concept approximation problems [Kloesgen and Żytkow, 2002]. In KDD, which is a sequence of iterative and interactive processes of dealing with vague concepts over imprecise, incomplete, noisy information (data), searching for approximation of concepts becomes a central problem. A great effort of many researchers has been done to design newer, faster and more efficient methods for solving concept approximation problem. Rough set theory has been introduced by [Pawlak, 1991] as a tool for concept approximation under uncertainty. The idea is to approximate the concept by two descriptive sets called lower and upper approximations. The lower and upper approximations must be extracted from available training data. The main philosophy of rough set approach to concept approximation