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

Savu Irina, Miculescu Radu, Mihail Alexandru

Demonstratio Mathematica

2023

Vol. 56, nr 1

art. no. 20220217

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.