Abstract
Preference relation is a usual preference elicitation structure in decision making problems, because of its simplicity and clarity for experts involved. However different issues related to preference elicitation make necessary to check that such relations have at least a minimal consistency to obtain meaningful decisions. Consistency of preference relations is related to rationality of experts' preferences and it ensures that their elicitation does not follow either a random or an illogical process. The lack of consistency leads to useless and wrong decisions. Hence the consistency checking of preference relations is a crucial and challenging issue across the decision process. Consequently multiple proposals have been introduced to study the consistency of preference relations. Keeping in mind the importance of consistency and taking into account the recent and high interest of hesitant fuzzy information in decision making with appearance of Hesitant Fuzzy Sets, this paper aims at establishing a clear taxonomy regarding the types of consistency of preference relations with hesitant information such as, hesitant fuzzy preference relation, hesitant multiplicative preference relation, and the extended hesitant fuzzy linguistic preference relation; pointing out those cases that make no sense to study, and proposing new definitions for the types of consistency when dealing with hesitant preference relations in those cases that either there have not been defined yet or in those ones in which current definitions can be improved.