Given a finite totally ordered set of linguistic terms, the operations intersection and connected union provide a lattice structure to the set of hesitant fuzzy linguistic term sets. In this framework, hesitant fuzzy linguistic descriptions of a given set of alternatives are considered. A distance between hesitant fuzzy linguistic descriptions is introduced based on the properties of the lattice. This metric structure allows distances between decision makers to be computed. A centroid or group representative is defined in group decision-making processes where decision makers are assessing different alternatives by means of hesitant fuzzy linguistic term sets.