On algorithm rules of interval grey numbers based on the “Kernel” and the degree of greyness of grey numbers

Abstract

Algorithm of grey numbers and grey algebraic system is the theoretical basis of grey system theory. It is possessed of very important significance in the developing course of grey system theory. A definition for grey “Kernel” has been put forward first. The algorithm axiom, algorithm rules of interval grey numbers and a new algebraic system is built based on the “Kernel” and the degree of greyness of grey numbers. And the properties of the algorithm are studied. Up to now, the algorithm of interval grey numbers have been transformed to algorithm of real numbers. So, the difficult problem for set up algorithm of interval grey numbers have been solved to a certain degree. The algorithm of interval grey numbers could be extended to the case of algorithm of grey algebraic equation, grey differential equation and grey matrix which including interval grey numbers. The algorithm system of interval grey numbers also opened a new passageway for research on grey input-output and grey programming, etc.