Iterated fuzzy set systems: A new approach to the inverse problem for fractals and other sets

CABRELLI, CARLOS A.; FORTE, BRUNO; MOLTER, URSULA M.; VRSCAY, EDWARD

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: Amsterdam; Año: 1992 vol. 171 p. 79 - 100

0022-247X

Images with grey or colour levels admit a natural representation in terms of fuzzysets, but without the usual probabilistic interpretation of the latter. We introducea fuzzy set approach which incorporates, in part, the technique of iterated functionsystems (IFS) for the construction, analysis, and/or approximation of typicallyfractal 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,?\phi: [0, I] --> [0, I] associated with the contractive maps W, ofthe IFS affords much greater flexibility in the generation of images as well as in theinverse problem.