This study aims to reflect the grey information coverage and complex interactions effect in digital economy development. Therefore, a multi-attribute decision making method based on the grey interaction relational degree of the normal cloud matrix (GIRD-NCM) model is pro-posed. First, the original information coverage grey numbers are transformed into normal cloud matrixes, and then a novel Minkowski distance between normal clouds is proposed by using different information principles. Second, the GIRD-NCM model is established according to the Choquet fuzzy integral and grey relational degree. ...