A characterization of the fuzzy fractals generated by an orbital fuzzy iterated function system

The paper proves the representation uu = ∨_{x∈[u]^*} ux = ∨_{x∈[u]_1} ux and, moreover, that these joins equal pointwise maxima (Theorem 3.9), via a careful argument that avoids unjustified interchange of suprema and grey-level maps and controls limits in d∞; see the definition of Z and seeds ux, the key identity Z[n](u) = ∨_{x∈[u]^*} Z[n](ux), and the final identification uu = wu with wu := ∨_{x∈[u]^*} ux . The candidate solution hinges on an incorrect general claim that the fuzzy Hutchinson–Barnsley operator Z preserves arbitrary pointwise joins (it does not under the paper’s admissible grey-level maps), and it conflates joins with maxima without verifying attainment; both points are handled correctly (and more delicately) in the paper via Proposition 3.4/Remark 3.5 and Proposition 3.8 .