Abstract
Characterizations of a hesitant fuzzy filter in a residuated lattice are considered. Given a hesitant fuzzy set, a new hesitant fuzzy filter of a residuated lattice is constructed. The notion of a hesitant fuzzy G-filter of a residuated lattice is introduced, and its characterizations are discussed. Conditions for a hesitant fuzzy filter to be a hesitant fuzzy G-filter are provided. Finally, the extension property of a hesitant fuzzy G-filter is established.