分数阶灰色累加生成算子与累减生成算子及互逆性

Mutual Invertibility of Fractional Order Grey Accumulating Generation Operator and Reducing Generation Operator

针对现有灰色预测模型主要以一阶累加生成序列作为建模序列,再累减还原为原始序列预测值,本文通过Gamma函数将累加生成算子和累减生成算子拓展到正实数领域,给出分数阶累加生成算子和分数阶累减生成算子的解析表达式,一阶和整数阶均是其特例,证明了两算子之间的互逆性.为建立分数阶灰色预测模型和拓宽灰色预测模型的应用范围提供理论基础.

Defter from the existing grey prediction model mainly using one order ac- cumulating generation sequence and get prediction value through reducing generation operator, this paper extend the integer order accumulating generation operator and reducing generation operator to positive real number style by the Gamma function. The fractional order grey accumulating generation operator and reducing generation operator also fit integer order. Then proof the properties of mutual invertibility of fractional order grey accumulating generation operator and reducing generation operator. Expanding the accumulating generation operator and reducing generation operator would help develop fractional order grey prediction model and widen the application fields of grey prediction model.