C. A. Cabrelli, B. Forte, U. M. Molter, E. R. Vrscay. Iterated fuzzy set systems: a new approach to the inverse problem for fractal and other sets. J. Math. Anal. and Appl, 17(4):465-486, 1993.
Images with grey or colour levels admit a natural representations in terms of fuzzy sets, but without the usual probabilistic interpretation of the latter. We introduce a fuzzy set approach which incorporates, in part, the technique of literated function systems (IFS) for the construction, analysis and/or approximation of typically fractal sets and images. The method represents a significant departure from IFS, especially in the interpretation of the resulting image. the introduction of "grey-level maps", (i : [0, 1] ( [0, 1] associated with the contractive maps, (i of the IFS affords much greater flexibilita in the generation of images as well in the inverse problem.
@article{CFMV93,
Author = {Cabrelli, C. A. and Forte, B. and Molter, U. M. and Vrscay, E. R.},
Title = {Iterated fuzzy set systems: a new approach to the inverse problem for fractal and other sets},
Journal = {J. Math. Anal. and Appl},
Volume = {17},
Number = {4},
Pages = {465--486},
Year = {1993}
}