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There are several extensions of fuzzy sets. Hesitant fuzzy sets are one of them. They are defined in terms of a set of membership degrees. For a typical hesitant fuzzy set, this set of membership degrees has a finite number of values. One of the motivations to introduce score functions was to rank alternatives. In this case, as the membership degrees are a set, the comparison of membership values does not lead, in general, to a total order. Score functions can be seen as functions that transform the set of membership degrees into a single membership value. In this way, we can construct the total order. In this article, we propose a general framework to define score functions for hesitant fuzzy sets based on fuzzy integrals. This framework permits to see most relevant indices as particular cases. Moreover, previous approaches focused on typical hesitant fuzzy sets. Our approach is more general in the sense that we can …