Research On Grey Fractal Model

As a new system theory aiming at self-similarity, the fractal theory has been studied by many scholars and engineers and successfully applied in many fields. However, during the development of systems science, more and more system researchers and engineers have come to realized that the fractal theory could no longer offer accurate and satisfying answers to many approximate fractal problems because of system disturbances. Therefore, another kind of research designated as fuzzy fractal theory aiming at approximate self-similarity has come upon the stage.Based on research on fractal theory and fuzzy fractal theory, a new fractal model designated as"grey fractal model"whose fractal dimension is defined as"grey fractal dimension"is presented in this paper, to directly cope with fractal problems of approximate self-similarity. Hence, the degree the grey fractal dimension is defined and in order to calculate the grey fractal dimension accurately, two different methods—linear regression method and fuzzy linear programming method are utilized. During research on the fractal characteristics of the hierarchical structure of Jiangsu urban system 2005, the grey fractal model is proved to outperform the fractal model and fuzzy fractal model in depicting and solving practical fractal problems.