@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 },
}