企业分形分布的判定和应用

Determination and application of fractal distribution of enterprises

采用行政区划国家标准建立了两个行业的δ-覆盖,并基于信息维数的定义,定量验证了企业分形分布的猜想,并测定了两个行业的分数维数.在此基础上将分数维数与嵌套区域秩序方法相结合,提出一种新的分形分布拟合方法FDF.经实际检验,FDF相比传统的方法,在所需数据量小、稳定性强、适应重点区域等方面,具有显著的特点和优势.最后,将该方法应用到一个调度实例问题,不仅给出了跨企业调度的优化范围,而且证明本文方法可以广泛应用于各类依赖于空间分布的企业协同研究.

The key problem whether enterprises are fractal distributed has not been solved though the concept of Fractal Company is widely accepted. Based on national standard of administrative divisions, this paper establishes the δ-covers of two industries and quantitatively proves that the enterprises are fractal distributed utilizing the definition of information dimension. Accordingly, a novel fitting method, - Fractal Distribution Fitting （FDF）, is developed utilizing the calculated fractal dimension and the ranks of the nested divisions. Experiments show that FDF is significantly superior to traditional fitting method due to its needs of fewer data with higher stability and better suitability for major divisions. Finally, FDF is applied to a case of obtaining optimized scope of scheduling jobs between enterprises. This method is proved to be adaptable to various domains of study on distribution - dependant coordination among enterprises.