A voltage sag severity index is the basis for sag assessment. Because the existing method does not consider the uncertainty and difference of the tolerance characteristics, this paper proposes an improved voltage sag severity interval assessment method for the user side. First, this paper explains the existing method and points out that it cannot reflect the uncertainty of the tolerance characteristics. To characterize the uncertainty, it uses interval number theory to modify the calculation method based on the uncertainty regions of typical sensitive equipment. Because the results of the traditional interval assessment method are conservative, it determines the interval weight and uses an affine algorithm to calculate the comprehensive severity interval index. Finally, it uses the measurement function to determine the site ranking. The IEEE 30-bus system is used for verification. The results show that the interval index can characterize the comprehensive sag level and dynamic tolerance characteristics of the user side. This work is supported by the Science and Technology Project of China Southern Power Grid Co., Ltd. (No. GZHKJXM20170141).