General grey numbers and their operations

Purpose – The purpose of this paper is to advance new rules about operations of grey numbers. Design/methodology/approach – The paper first puts forward the definitions of basic element of grey number and general grey number. The operation axion, operation rules of general grey numbers and a new algebraic system for general grey numbers are built based on the “kernel” and the degree of greyness of grey numbers. Findings – Up to now, the operation of general grey numbers has been transformed to operation of real numbers; thus, the difficult problem for set up operation of general grey numbers has been solved to a certain degree. Practical implications – The method exposed in the paper can be used to integrate information from a different source. The operation of general grey numbers could be extended to the case of grey algebraic equation, grey differential equation and grey matrix which includes general grey numbers. The operation system of general grey numbers also opened a new passageway for research on grey input-output and grey programming, etc. Originality/value – The new conception of a basic element of grey number and general grey number was given for the first time in this paper. The novel operation rules of general grey numbers were also constructed. Keywords Basic element, General grey numbers, Operations, Kernel, Greyness, Number theory, Mathematical programming Paper type Research paper