@InProceedings{Petrik:ISCAMI2009, IS = { zkontrolovano 29 Jan 2010 }, UPDATE = { 2009-09-29 }, author = { Petr{\'\i}k, Milan and Sarkoci, Peter }, title = { Differential properties of strict triangular norms along zero }, year = { 2009 }, pages = { 43--60 }, booktitle = { ISCAMI 2009: International Student Conference on Applied Mathematics and Informatics }, editor = { Nov{\'a}k, Vil{\'e}m and Perfilieva, Irina and {\v S}t{\v e}pni{\v c}ka, Martin }, publisher = { Institute for Research and Applications of Fuzzy Modeling, University of Ostrava }, address = { Ostrava, Czech Republic }, book_pages = { 59 }, month = { May }, day = { 13--15 }, venue = { Malenovice, Czech Republic }, annote = { Differential properties of strict triangular norms (shortly, strict t-norms) along their ``zero borders'' are investigated. For this purpose we utilize the notion of the ``order of infinite smallness'' introduced by Jarn{\'\i}k. For a strict t-norm T, described by its multiplicative generator theta, we define a function b_T:(0,1)^2 to (0,1) as b_T(y)= lim_(x - 0_+) T(x,y)/x. If the function b_T is well defined then, according to the order of infinite smallness of theta in zero, it can behave in exactly one the the following ways. If the order of infinite smallness of theta in zero, denoted by p, is 0 then b_T is a constant 1. If p in (0,infinity) then b_T is a bijection. If p=infinity then b_T is a constant 0. Moreover, if b_T is a bijection then it accords directly with theta^p and thus with one of the multiplicative generators of the strict t-norm. Besides the possibility of recostructing multiplicative generators from the shape of some strict t-norms, these results give some insight into the question of convex combinations of strict t-norms. }, keywords = { strict triangular norm, multiplicative generator, associative function }, prestige = { local }, authorship = { 50-50 }, project = { GACR 401/09/H007 }, www = { http://irafm.osu.cz/iscami }, note = { abstract }, }