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A topological approach to fuzzy iterated function systems
Taras Banakh, Krzysztof Caban, Filip Strobin
https://arxiv.org/abs/2509.23669 https://arxiv.org/p…

A topological approach to fuzzy iterated function systems
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 $\mathcal{K}_{\mathcal{F}}(X)$ of all compact fuzzy sets. As a consequence, we prove that a fuzzy IFS on a Hausdorff topological space which is topologically contracting admit…