Distance and similarity measures for higher order hesitant fuzzy sets

In this study, we extend the hesitant fuzzy set (HFS) to its higher order type and refer to it as the higher order hesitant fuzzy set (HOHFS). HOHFS is the actual extension of HFS that enables us to define the membership of a given element in terms of several possible generalized type of fuzzy sets (G-Type FSs). The rationale behind HOHFS can be seen in the case that the decision makers are not satisfied by providing exact values for the membership degrees and therefore the HFS is not applicable. However, in order to indicate HOHFSs have a good performance in decision making, we first introduce some information measures for HOHFSs and then apply them to multiple attribute decision making with higher order hesitant fuzzy information.