Abstract: As the society and economy developing, more and more problems need to use interval grey number. Aiming at the situation that the turn point of the whitenization function must be real number, the method of building and calculating the function when the turn point is an interval grey number was discussed in this paper. Firstly, this paper constructed weight function with interval gray number was constructed through defining the standardized methods of the interval grey number. Then use the standardized interval grey number replace the real number of the whitenization function. And the expression of the whitenization function with interval grey number was given. Secondly, discuss the two circumstances that there was only one interval grey number in the piecewise curve of the whitening function or two endpoints were both interval grey numbers. And when the four turn points were all interval grey numbers, the expression of whitenization function f_j^k(⊗) was given. At last, the interval grey clusters model was used to evaluate the core competencies of eight private enterprises in Xuchang. Our group had investigated the eight enterprises to get the data. And twenty experts had been asked to build the whitenization function. The result indicated the model is effective and reasonable.

Key words: grey clusters, interval grey number, whitenization function, standardization