FDGM (1, 1) model based on unified fractional grey generation operator. Grey Systems: Theory and Application

Purpose The purpose of this paper is to unify the expression of fractional grey accumulating generation operator and the reducing generation operator, and build the FDGM(1,1) model with the unified fractional grey generation operator.

Design/methodology/approach By systematically studying the properties of the fractional accumulating operator and the reducing operator, and analyzing the sensitivity of the order value, a unified expression of the fractional operators is given. The FDGM(1,1) model with the unified fractional grey generation operator is established. The relationship between the order value and the modeling error distribution is studied.

Findings The expression of the fractional accumulating generation operator and the reducing generation operator can be unified to a simple expression. For −1<r < 1, the fractional grey generation operator satisfies the principle of new information priority. The DGM(1,1) model is a special case of the FDGM(1,1) model with r = 1.

Research limitations/implications The sensitivity of the unified operator is verified through random numerical simulation method, and the theoretical proof was not yet possible.

Practical implications The FDGM(1,1) model has a higher modeling accuracy and modeling adaptability than the DGM(1,1) by optimizing the order.

Originality/value The expression of the fractional accumulating generation operator and the reducing generation operator is firstly unified. The FDGM(1,1) model with the unified fractional grey generation operator is firstly established. The unification of the fractional accumulating operator and the reducing operator improved the theoretical basis of grey generation operator.