Fuzzy GUHA

The GUHA method is one of the oldest methods of exploratory data analysis, which is regarded as part of the data mining or knowledge discovery in databases (KDD) scienti_c area. Unlike many other methods of data mining, the GUHA method has firm theoretical foundations in logic and statistics. In scope of the method, finding interesting knowledge corresponds to finding special formulas in satisfactory rich logical calculus, which is called observational calculus. The main topic of the thesis is application of the "fuzzy paradigm" to the GUHA method By the term "fuzzy paradigm" we mean approaches that use many-valued membership degrees or truth values, namely fuzzy set theory and fuzzy logic. The thesis does not aim to cover all the aspects of this application, it emphasises mainly on: - Association rules as the most prevalent type of formulas mined by the GUHA method - Usage of fuzzy data - Logical aspects of fuzzy association rules mining - Comparison of the GUHA theory to the mainstream fuzzy association rules - Implementation of the theory using the bit string approach The thesis throughoutly elaborates the theory of fuzzy association rules, both using the theoretical apparatus of fuzzy set theory and fuzzy logic. Fuzzy set theory is used mainly to compare the GUHA method to existing mainstream approaches to formalize fuzzy association rules, which were studied in detail. Fuzzy logic is used to define novel class of logical calculi called logical calculi of fuzzy association rules (LCFAR) for logical representation of fuzzy association rules. The problem of existence of deduction rules in LCFAR is dealt in depth. Suitable part of the proposed theory is implemented in the Ferda system using the bit string approach. In the approach, characteristics of examined objects are represented as strings of bits, which in the crisp case enables efficient computation. In order to maintain this feature also in the fuzzy case, a profound low level testing of data structures and algoritms for fuzzy bit strings have been carried out as a part of the thesis.