ITERATED FUZZY SET SYSTEMS - A NEW APPROACH TO THE INVERSE PROBLEM FOR FRACTALS AND OTHER SETS

Images with grey or colour levels admit a natural representation 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 iterated 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," θ{symbol}i: [0, 1] → [0, 1] associated with the contractive maps wi of the IFS affords much greater flexibility in the generation of images as well as in the inverse problem. © 1992.