2025/09/28 by Banakh, Taras, Caban, Krzysztof, Strobin, Filip
#03E72 #28A80 #47H09 #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.2509.23669
In the paper we unify two extensions of the classical Hutchinson--Barnsley theory - the topological and the fuzzy-set approaches. We show that a fuzzy iterated function system (fuzzy IFS) on a Tychonoff space X which is contracting w.r.t. some admissible multimetric, generates a natural fuzzy attractor in the hyperspace KF(X) of all compact fuzzy sets. As a consequence, we prove that a fuzzy IFS on a Hausdorff topological space which is topologically contracting admits a fuzzy attractor in a bit weaker sense. Our discussion involves investigations on topologies on the hyperspace KF(X) which are suitable for establishing convergence of sequences of iterations of a fuzzy Hutchinson operator.