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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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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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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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