This paper studies the structural problems of kernel and grayness of interval gray numbers under the known whitening weight function. Firstly, the definition of kernel and gray scale reconstruction of the interval grey number is given. The kernel and grayness of the union of grey numbers are proposed, and their correlation properties are analyzed. Then, the kernel and gray scale are discussed when the interval grey number is a typical function of the white power. Particularly, when the whitening weight function is reduced to being one within the interval grey number, namely the grey number is lack of the distribution information, the results of the kernel and the grayness are consistent with the original definition. The proposed kernel and gray level are extended to the existing research.