Fuzzy-set approach to invariant idempotent measures

We provide a new approach to the Hutchinson-Barnsley theory for idempotent measures first presented in Mazurenko and Zarichnyi (2018) [24]. The main feature developed here is metrization of space using embedding fuzzy sets. metric obtained induces topology stronger than canonical pointwise convergence topology. A key result existence bijection between sets conjugation Markov operator an IFS on fractal associated Fuzzy IFS. This allows prove that contraction w.r.t. induced and, from this, obtain theorem algorithms draw pictures invariant as grayscale images.