分数阶灰色累加生成算子性质研究

数据序列满足灰指数规律是灰色预测模型的建模条件,灰色系统理论通过累加生成方法弱化数据随机性,通过累加生成算子使得原始数据序列满足近似指数规律;分数阶累加生成算子是建立分数阶灰色预测模型的基础,利用Gamma函数给出一阶累加生成算子推导出整数阶累加生成算子与分数阶累加生成算子的详细步骤,并证明了分数阶灰色累加生成算子满足不动点定理、信息优先原理、交换律和指数律等重要性质;通过数值实例给出了分数阶累加生成算子的数据变化趋势,并验证了分数阶灰色累加生成算子满足不动点定理、交换律和指数律性质;研究方法与分数阶灰色累加算子性质有助于丰富分数阶灰色算子理论,为分数阶灰色预测模型奠定理论基础。

Study on the Properties of Fractional Order Grey Accumulating Generation Operator

The fact that the data sequence satisfies the grey exponential law is the modeling condition of the grey prediction model. The grey system theory weakens the randomness of data by accumulating generation method. The fractional order accumulating generation operator is the basis for establishing the fractional order grey prediction model. By the Gamma function, the detailed proof steps of the integer order accumulating generation operator and fractional order accumulating generation operator based on the first order accumulating generation operator are given. The properties of fractional grey accumulating generation operator that satisfy the important properties such as fixed point theorem, information priority principle, exchange law and exponential law are proved. The data changing trend of the fractional order accumulating generation operator is given by numerical example. The properties of fixed point theorem, commutative law and exponential law of fractional order grey accumulating generator are verified by numerical example. The research method and properties are helpful for the theory of fractional order grey operators and fractional order grey prediction model.