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Fuzzy implications
Jirmusová, Veronika ; Zbořil, František (referee) ; Hliněná, Dana (advisor)
This thesis deals with fuzzy logical connectives, focusing in particular on fuzzy implications and their constructions. Two new classes of fuzzy implications were discovered through the construction of fuzzy implications using the -transformation. Additionally, an experiment was conducted to model fuzzy logical connectives based on empirical data, utilizing the approximation of the additive generator. A fuzzy implication was modeled using the approximated data. The experiment also inquires into how people perceived fuzzy implications in everyday language, whether they perceive them as equivalence, and whether the modeled implication resembles any known fuzzy implication.
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Fuzzy graphs theory
Ducký, Patrik ; Zbořil, František (referee) ; Hliněná, Dana (advisor)
This bachelor thesis deals with the problems of fuzzy sets, fuzzy relations and their application in fuzzy graph theory. In the introduction, the basic problem of fuzzy sets is introduced. The next part of the thesis is devoted to the properties of fuzzy relations and their relation to fuzzy graphs. The main part of the thesis consists of classical coloring, fractional coloring of graphs and their fuzzification. Finally, an application is presented that can instruct the user on fractional coloring of fuzzy graphs, and at the same time can color the input fuzzy graph. The goal of this thesis and the application is to contribute to the awareness of this issue and its possible applications in computer science.
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Conjuction and Disjunction in Fuzzy Logic
Havlena, Vojtěch ; Kunovský, Jiří (referee) ; Křena, Bohuslav (advisor)
This thesis deals with triangular norms and their generalizations - uninorms, in particular with their transformation using a unit function and also with modeling of fuzzy conjunction and disjunction based on empirical data. The conditions under which transformations of certain uninorms give again uninorms are established. Conditions of invariance transformations for certain class of uninorms are found. Transformations of uninorms extend class of connectives. The study of these transformations faciliates the search of modeling conditions. An algorithm for modeling of fuzzy connectors is also proposed and analyzed. An experiment based on implementation of the algorithm is evaluated. This experiment aims at modeling of fuzzy conjunction for human use.
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Negation in Fuzzy Logic
Dekrét, Lukáš ; Havlena, Vojtěch (referee) ; Křena, Bohuslav (advisor)
This thesis deals with fuzzy logical connections, mainly negations, their properties and constructions.We focused our attention on triangular norms and conorms, which are often used for modeling of fuzzy conjunction and disjunction.We showed the possibilities of constructions of triangular norm and conorm using involutive negations.Futhermore, we dealed with approximation of function, which was created using empirical data to well known fuzzy negator.
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Negation in Fuzzy Logic
Dekrét, Lukáš ; Havlena, Vojtěch (referee) ; Křena, Bohuslav (advisor)
This thesis deals with fuzzy logical connections, mainly negations, their properties and constructions.We focused our attention on triangular norms and conorms, which are often used for modeling of fuzzy conjunction and disjunction.We showed the possibilities of constructions of triangular norm and conorm using involutive negations.Futhermore, we dealed with approximation of function, which was created using empirical data to well known fuzzy negator.
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Conjuction and Disjunction in Fuzzy Logic
Havlena, Vojtěch ; Kunovský, Jiří (referee) ; Křena, Bohuslav (advisor)
This thesis deals with triangular norms and their generalizations - uninorms, in particular with their transformation using a unit function and also with modeling of fuzzy conjunction and disjunction based on empirical data. The conditions under which transformations of certain uninorms give again uninorms are established. Conditions of invariance transformations for certain class of uninorms are found. Transformations of uninorms extend class of connectives. The study of these transformations faciliates the search of modeling conditions. An algorithm for modeling of fuzzy connectors is also proposed and analyzed. An experiment based on implementation of the algorithm is evaluated. This experiment aims at modeling of fuzzy conjunction for human use.
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