In practical applications, pieces of evidence originated from different sources might be modeled by different uncertainty theories. To implement the evidence combination under the Dempster–Shafer evidence theory(DST) framework, transformations from the other type of uncertainty representation into the basic belief assignment are needed. a-Cut is an important approach to transforming a fuzzy membership function into a basic belief assignment, which provides a bridge between the fuzzy set theory and the DST. Some drawbacks of the traditional a-cut approach caused by its normalization step are pointed out in this paper. An improved a-cut approach is proposed, which can counteract the drawbacks of the traditional a-cut approach and has good properties. Illustrative examples, experiments and related analyses are provided to show the rationality of the improved a-cut approach. In practical applications, pieces of evidence originated from different sources might be modeled by different uncertainty theories. To implement the evidence combination under the Dempster-Shafer evidence theory (DST) framework, transformations from the other type of uncertainty representation into the basic belief assignment are needed. a-Cut is an important approach to transforming a fuzzy membership function into a basic belief assignment, which provides a bridge between the fuzzy set theory and the DST. Some drawbacks of the traditional a-cut approach caused by its normalization step are pointed out of this paper. An improved a-cut approach is proposed, which can counteract the drawbacks of the traditional a-cut approach and has good properties. Illustrative examples, experiments and related analyzes are provided to show the rationality of the improved a-cut approach.