Non-dual fuzzy connections

The lack of double negation and de Morgan properties makes fuzzy logic unsymmetrical. This is the reason why fuzzy versions of notions like closure operator or Galois connection deserve attention for both antiotone and isotone cases, since they are not dual. This paper offers them attention, comming to the following conclusions: some kind of hardly describable ”local preduality” still makes possible important parallel results; interesting new concepts besides antitone and isotone ones (like, for instance, residuated pair), that were classically reducible to the latter, gain independency in fuzzy setting.