On Uncertainty Measures of the Interval-Valued Hesitant Fuzzy Set

Interval-valued hesitant fuzzy sets (IVHFS), as a kind of decision information presenting tool which is more complicated and more scientific and more elastic, have an important practical value in multiattribute decision-making. There is little research on the uncertainty of IVHFS. The existing uncertainty measure cannot distinguish different IVHFS in some contexts. In my opinion, for an IVHFS, there should exist two types of uncertainty: one is the fuzziness of an IVHFS and the other is the nonspecificity of the IVHFS. To the best of our knowledge, the existing index to measure the uncertainty of IVHFS all are single indexes, which could not consider the two facets of an IVHFS. First, a review is given on the entropy of the interval-valued hesitant fuzzy set, and the fact that existing research cannot distinguish different interval-valued hesitant fuzzy sets in some circumstances is pointed out. With regard to the uncertainty measures of the interval-valued hesitant fuzzy set, we propose a two-tuple index to measure it. One index is used to measure the fuzziness of the interval-valued hesitant fuzzy set, and the other index is used to measure the nonspecificity of it. The method to construct the index is also given. The proposed two-tuple index can make up the fault of the existing interval-valued hesitant fuzzy set's entropy measure.