The proposal of hesitant fuzzy sets provides a considerable mathematical method for dealing with uncertain, inaccurate data and knowledge that cannot be correctly captured by other fuzzy sets. In this paper, the hesitant \(L-\) fuzzy sets over distributive lattices are studied, and the elements of the hesitant \(L-\) fuzzy sets are considered as the sublattices of the distributive lattices, which are named as the hesitant \(L_S-\) fuzzy sets. Before studying hesitant \(L_S-\) fuzzy sets, this paper first discusses the truth set \(L _ S\) in terms of given logical operations and order relations, and studies whether the truth set \(L_S\) and \(L_{CS}\) can form posets or lattices under some order relations. Furthermore, the concept of hesitant \(L_S-\) fuzzy sets and the corresponding concepts of \(\alpha -\) level sets and strong \(\alpha -\) level sets are proposed, and their related properties are studied. In the course of the study, this paper also points out the loopholes of Dehmiry et al. in the study of hesitant \(L-\) fuzzy sets, such as logical operations and order relations, and makes corrections.
