Fuzzy attractors appearing from GIFZS

Cabrelli, Forte, Molter and Vrscay in 1992 considered a fuzzy version of the theory of iterated function systems (IFSs in short) and their fractals, which now is quite rich and important part of the fractals theory. On the other hand, Miculescu and Mihail in 2008 introduced another generalization of the IFSs' theory - instead of selfmaps of a metric space X, they considered mappings defined on the finite Cartesian product Xm. In this paper we show that the fuzzification ideas of Cabrelli et al. can be naturally adjusted to the case of mappings defined on finite Cartesian product. In particular, we define the notion of a generalized iterated fuzzy function system (GIFZS in short) and prove that it generates a unique fuzzy fractal set. We also study some basic properties of GIFZSs and their fractals, and consider the question whether our setting gives us some new fuzzy fractal sets.