Interval Grey Hesitant Fuzzy Set and Its Applications in Decision-Making

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 hesitant fuzzy set (IGHFS), in which possible degrees of grey numbers are designed to indicate the upper and lower limits of the interval number. Meanwhile, its basic operational laws, score function, entropy method, and distance measures are proposed. And then, a multicriteria decision-making (MCDM) model IGHFS-TOPSIS is developed based on them. Finally, an example of MOOC platform selection issues for teaching courses illustrates the effectiveness and feasibility of the decision model under the IGHFS.