A greyness reduction framework for prediction of grey heterogeneous data

Abstract

Existing operational rules of interval grey numbers do not make full use of possible background information when determining the interval boundaries, and this may result in inconsistent results if applying different logical operations. This paper finds that multiplication and division rules of interval grey numbers do not meet the calculation rule of inverse operators. Direct solution and inverse solution of the same interval grey number object may differ not only in numerical ranges but also in greyness degrees. To improve the accuracy of grey number calculation, new operational rules for multiplication and division of interval grey numbers are proposed. Then the traditional prediction modelling method of grey heterogeneous data is refined and expanded by integrating a greyness reduction preprocessing, which is based on the proposed calculation rules. Application of the expanded heterogeneous interval grey number prediction model to a stock replenishment scheduling problem in emergency rescue scenarios is included to illustrate the new operational rules of grey numbers and their application in prediction algorithm, and the proposed approach is compared with other existing methods to demonstrate its effectiveness.