Normalized Geometric Bonferroni Operators of Hesitant Fuzzy Sets and Their Application in Multiple Attribute Decision Making

The Bonferroni Mean (BM) is a very useful aggregation technique, because it can capture the interrelation-ship between input arguments. Many BM type operators have been proposed, such as the weighted BM, the generalized BM, the intuitionistic fuzzy BM, and so on. However, the geometric BM for Hesitant Fuzzy Sets (HFSs) hasn’t been studied. In this paper, based on the geometric mean and the BM, we will propose two normalized weighted geometric BMs, and they can reect the interrelationship between the individual criterion and other criterion, which is the main advantage of the BM. Then, we will study some properties of the proposed operators, and apply them to deal with Multiple Attribute Decision Making (MADM) problems under the hesitant fuzzy environments. Finally, an example is presented to verify the developed approach.