The constitutive error and optimize operator research in the grey number's addition and subtraction inverse operation

At first, this paper defined the grey number inverse operation, proposed a essential condition about the grey number's addition and subtraction inverse operation, then discovered the constitutive error in process of the addition and subtraction inverse operation that is the generally result in the addition and subtraction inverse operation enlarges the length to \b − a\ in the top and bottom sector comparing to the exact solution. The author has introduced a kind Optimize Operator (b − a) − 2(b − a)r that is based on the standard grey number for eliminating this kind of constitutive error in the inverse operation, which was properly used in three forms of addition and subtraction inverse operation. At last, the author confirmed this method's feasibility and usability through a classical example.