Using the fractional order method to generalize strengthening buffer operator and weakening buffer operator

To reveal the relationship between a weakening buffer operator and strengthening buffer operator, the traditional integer order buffer operator is extended to one that is fractional order. Fractional order buffer operator not only can generalize the weakening buffer operator and the strengthening buffer operator, but also results in small adjustments of the buffer effect. The effectiveness of the grey model ( GM ( 1,1) ) with the fractional order buffer operator is validated by six cases.