Modeling mechanism of a novel fractional grey model based on matrix analysis

Abstract

To fully display the modeling mechanism of the novel fractional order grey model (FGM (q,1)), this paper decomposes the data matrix of the model into the mean generation matrix, the accumulative generation matrix and the raw data matrix, which are consistent with the fractional order accumulative grey model (FAGM (1,1)). Following this, this paper decomposes the accumulative data difference matrix into the accumulative generation matrix, the q-order reductive accumulative matrix and the raw data matrix, and then combines the least square method, finding that the differential order affects the model parameters only by affecting the formation of differential sequences. This paper then summarizes matrix decomposition of some special sequences, such as the sequence generated by the strengthening and weakening operators, the jumping sequence, and the non-equidistance sequence. Finally, this paper expresses the influences of the raw data transformation, the accumulation sequence transformation, and the differential matrix transformation on the model parameters as matrices, and takes the non-equidistance sequence as an example to show the modeling mechanism.