关键词: 剩余格, 犹豫模糊集, 犹豫模糊（蕴涵、正定蕴涵、MV、正规）滤子, 犹豫模糊集的水平集

Abstract: By applying hesitant fuzzy set to the filter theory of residuated lattices, this paper proposes the concepts of hesitant fuzzy filters, hesitant fuzzy implicative filters, hesitant fuzzy positive implicative filter, hesitant fuzzy MV-filters and hesitant fuzzy regular filters of residuated lattices, investigates their properties, discusses their relations, and obtains some equivalent characterizations between them. Then, this paper gives the conditions for a hesitant fuzzy set translating into a hesitant fuzzy filter and for a hesitant fuzzy filter translating into a hesitant fuzzy (positive implicative, MV, regular) implicative filter. Finally, this paper studies the relations between kinds of filters and its corresponding level filters, and establishes the extension theorems of hesitant fuzzy Boolean filters and hesitant fuzzy regular filters of residuated lattices.

Key words: residuated lattice, hesitant fuzzy set, hesitant fuzzy (implicative, positive implicative, MV, regular) filter; , level sets of a hesitant fuzzy set