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Integrated development environment for Artificial Intelligence Fuzzy Numbers Module
Pergl, Miroslav ; Hrabec, Jakub (referee) ; Jirsík, Václav (advisor)
Master’s thesis deals with mathematical operation with fuzzy numbers. The first part of the thesis deals with theoretical knowledge of fuzzy arithmetic and defines fuzzy sets, fuzzy numbers, universum and five membership function used in program. In the concrete it describes – cut method for dealing with fuzzy numbers as with limited interval for specific level which simplifies computation. The second part of the thesis contains description of programmed module for mathematical operation with fuzzy numbers. There is described creation of user interface which is using to set parameters of computation. There are also described support functions which make operation with fuzzy numbers possible and operation ensures output.
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Classification of microsleep by means of analysis EEG signal
Ronzhina, Marina ; Smital, Lukáš (referee) ; Čmiel, Vratislav (advisor)
This master thesis deals with detection of microsleep on the basis of the changes in power spectrum of EEG signal. The results of time-frequency analysis are input values for the classifikation. Proposed classification method uses fuzzy logic. Four classifiers were designed, which are based on a fuzzy inference systems, that are differ in rule base. The results of fuzzy clustering are used for the design of rule premises membership functions. The two classifiers microsleep detection use only alpha band of the EEG signal’s spectrogram then allows the detection of the relaxation state of a person. Unlike to first and second classifiers, the third classifier is supplemented with rules for the delta band, which makes it possible to distinguish the 3 states: vigilance, relaxation and somnolence. The fourth classifier inference system includes the rules for the whole spectrum band. The method was implemented by computer. The program with a graphical user interface was created.
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Fuzzy Petri Nets for Expert systems
Maksant, Jindřich ; Valenta, Jan (referee) ; Jirsík, Václav (advisor)
The object of this thesis is proposal and practical implementation of expert system, whose knowledge base will be modeling by fuzzy Petri nets. The proposal is based on knowledge in theoretical analysis of diagnostic expert system and fuzzy Petri nets. This proposal is realised in programming language C#. There are described functions of program and it is made a model consultation with using two different knowledge base.
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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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Two Connections between Epistemic and Fuzzy Logics
Běhounek, Libor
Two possible connections between epistemic and fuzzy logics are studied. Epistemic fuzzy logic as a kind of modal logic studies the reasoning of agents about fuzzy propositions; problems of such a synthesis caused by the invalidity of the axiom K are hinted at. Another direction is to found epistemic on fuzzy logic; the paper sketches the way how representing feasible knowledge as a fuzzy modality eliminated the logical omniscience paradox.
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Automatické dokazování ve fuzzy logikách
Cintula, Petr ; Navara, M.
Computer algebra allows to perform many operations which were considered difficult, e.g., factorization, integration, symbolic solution of ODEs, etc. Logical operations are not always implemented. E.g., Maple 9 has a package LOGIC which was missing in several preceding versions. Except for packages for fuzzy control, there seems to be no professional software for fuzzy logical tasks. Here we summarize current situation in computer algebra support of testing tautologies in fuzzy logics.
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Slabě implikační predikátové fuzzy logiky
Cintula, Petr
There are two classes of propositional logics related to the area of mathematical fuzzy logics proposed in work of the author (see also joint paper by the author and Libor Běhounek where philosophical, methodological, and pragmatical reasons for introducing these two classes appear.) After we recall same basic definitions we turn our attention to the first-order variants of these two classes of logics. The results presented here are mainly from the author's thesis and his upcoming paper. Because of the lack of space we present the basic definitions and theorems only and we completely disregard the important concept of Baaz delta.
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