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

Abstract In this article, we present a structure result concerning fuzzy fractals generated by an orbital iterated function system ( X , d ) f i ∈ I ρ \left(\left(X,d),{({f}_{i})}_{i\in I},{\left({\rho }_{i})}_{i\in I}) . Our involves the following two main ingredients: (a) fractal associated with canonical N mathvariant="normal">Λ τ \left(\left({I}^{{\mathbb{N}}},{d}_{\Lambda }),{\left({\tau , where {d}_{\Lambda } is Baire’s metric on code space {I}^{{\mathbb{N}}} and : → {\tau }_{i}:{I}^{{\mathbb{N}}}\to given ω 1 2 … ≔ }_{i}\left(\left({\omega }_{1},{\omega }_{2},\ldots )):= \left(i,{\omega ) for every \left({\omega )\in i\in I ; (b) projections of certain systems under consideration.