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In a previous paper we introduced hesitant fuzzy sets. A typical hesitant fuzzy set (HFS) assigns a finite set of membership values to each element. Because of that, in general, the comparison of the membership of different elements to the same set does not lead to a total order. In this paper we study the definition of score functions. Score functions were introduced for HFS. They are functions that summarize the membership values of a given element to the fuzzy set and allows us to build this total order for hesitant fuzzy sets. We propose a new index based on the Choquet integral and we compare this approach with some existing indices in the literature.