@InProceedings{Petrik:ISCAM2007, IS = { zkontrolovano 15 Dec 2007 }, UPDATE = { 2007-12-11 }, author = { Petr{\'\i}k, Milan }, title = { Reconstruction of multiplicative and additive generators of strict t-norms }, year = { 2007 }, pages = { 31--32 }, booktitle = { ISCAM 2007: International Conference in Applied Mathematics for Undergraduate and Graduate Students }, editor = { Bogn{\'a}r, Tom{\'a}{\v s} and {\v C}ipkov{\'a}, Karla and Zajac, Michal }, publisher = { FEI, Slovak University of Technology }, address = { Bratislava, Slovakia }, book_pages = { 48 }, month = { April }, day = { 20--21 }, venue = { Bratislava, Slovakia }, annote = { Having a multiplicative resp. additive generator, it is easy to construct the corresponding strict t-norm. We have posed the inverse question: how can we reconstruct the multiplicative resp. additive generator if we have a strict t-norm defined. We give two methods for reconstruction of multiplicative resp. additive generators for two classes of strict t-norms. The first class is characterized by existence of a multiplicative generator g such that g'(0) in 0-inf. We show that in this case the shape of the multiplicative generator corresponds to the shape of the t-norm in the neighbourhood of the axis given by equations x=0 or y=0. The next class is characterized by existence of an additive generator t such that t'(1) in 0-inf. The shape of the additive generator corresponds, in this case, to the shape of the t-norm in the neighbourhood of the axis given by equations x=1 or y=1. }, keywords = { fuzzy logic, t-norm, associative function }, prestige = { local }, authorship = { 100 }, project = { GACR 201/07/1136 }, www = { http://zeus.elf.stuba.sk/Katedry/KM/iscam/ }, }