@misc{Baczyński_Michał_Krzysztof._Autor_Laws_2013, author={Baczyński, Michał Krzysztof. Autor and Grzegorzewski, Przemysław Wojciech. Autor and Niemyska, Wanda Helena. Autor}, copyright={Creative Commons Attribution BY 4.0 license}, address={Warszawa}, journal={Raport Badawczy = Research Report}, howpublished={online}, year={2013}, publisher={Instytut Badań Systemowych. Polska Akademia Nauk}, publisher={Systems Research Institute. Polish Academy of Sciences}, language={eng}, abstract={Recently, Grzegorzewski [5-7] introduced two new families of fuzzy implication functions called probabilistic implication and prob­abilistic S-implications. They are based on conditional copulas and make a bridge between probability theory and fuzzy logic. In the same arti­cle [7] author gives a motivation to his idea and indicates some interest­ing connections between new families of implications and the dependence structure of the underlying environment. In this paper the laws of con­traposition and the law of importation are studied for these families of fuzzy implications.}, type={Text}, title={Laws of Contraposition and Law of Importation for Probabilistic Implications and Probabilistic S-Implications}, keywords={Fuzzy implications, Probabilistic implications, Laws of contraposition, Law of importation, Functional equations, Implikacje rozmyte, Implikacje probabilistyczne, Prawa transpozycji, Prawo importu, Równania funkcyjne}, }