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Probabilistic representation of spatial fuzzy sets
Soukup, Lubomír
Membership function of a given fuzzy set is expressed by probability that a point belongs in the fuzzy set. Such a membership function is derived from probability distribution of points on the boundary of the fuzzy set. Polygonal boundary is considered. Spatial operations (conjunction, disjunction, complement) are defined accordingly. Several application areas are mentioned, namely classification of land cover, cadastral mapping, material quality analysis, interferometric monitoring of bridges.
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Modern trends in the area of computer physics
SURYNEK, Radek
The theme of the thesis is to make a list few fundamental modern methods which can be used in computerized physics. The thesis describes parallel computing, neural networks,genetic algorithms, fuzzy logic. Every chapter include theoretical description, simplified mathematical expression, proposals of technical solution. Applications are briefly mentioned here too. The printed matter is completed with a few simple examples. The closing part of the thesis acquired information about these methods and outlines their future development.
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Fuzzy GUHA
Ralbovský, Martin ; Rauch, Jan (advisor) ; Svátek, Vojtěch (referee) ; Holeňa, Martin (referee) ; Vojtáš, Peter (referee)
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.
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