The use of interval-valued hesitant fuzzy sets (IVHFS) can aid decision-makers in evaluating a variable using multiple interval numbers, making it a valuable tool for addressing decision-making problems. However, it fails to obtain information with greyness. The grey fuzzy set (GFS) can improve this problem but studies on it have lost the advantages of IVHFS. In order to improve the accuracy of decision-making and obtain more reasonable results, it is important to enhance the description of real-life information. We combined IVHFS and GFS and defined a novel fuzzy set named interval grey hesit...