Abstract: Based on the research of fractal theory and fuzzy fractal theory,a new fractal model with grey number dimension has been presented in this paper,to cope with approximate fractal problems which abound in reality. In order to calculate the grey number dimension,a fuzzy programming method has been applied. Moreover,it has been preliminarily and practically proved that this grey fractal model did have a better performance over the traditional fractal model and the fuzzy fractal model in depicting and solving certain fractal problem.

Key words: fractal, fuzzy fractal, grey number dimension, fuzzy programming