The structure of fuzzy fractals generated by an orbital fuzzy iterated function system

In this article, we present a structure result concerning fuzzy fractals generated by an orbital fuzzy iterated function system ((X,d),(ƒi)i∈I,(ρi)i∈I) . Our result involves the following two main ingredients: (a) the fuzzy fractal associated with the canonical iterated fuzzy function system ((IN,dΛ),(τi)i∈I,(ρi)i∈I) , where dΛ is Baire’s metric on the code space IN and τi:IN→IN is given by τi((ω1,ω2,…))≔(i,ω1,ω2,…) for every (ω1,ω2,…)∈IN and every i∈I ; (b) the canonical projections of certain iterated function systems associated with the fuzzy fractal under consideration.

---

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).