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

摘要： 将犹豫模糊集概念应用于剩余格的滤子理论中，提出了剩余格的犹豫模糊滤子、犹豫模糊蕴涵滤子、犹豫模糊正定蕴涵滤子、犹豫模糊MV-滤子及犹豫模糊正规滤子的概念，研究了它们的性质，讨论了它们之间的关系，获得了它们的若干等价刻画。给出了犹豫模糊集成为犹豫模糊滤子，及犹豫模糊滤子成为犹豫模糊（正定蕴涵、MV、正规）蕴涵滤子的条件。探究了各种犹豫模糊滤子与其对应的水平滤子之间的关系，建立了剩余格的犹豫模糊Boolean滤子和犹豫模糊正规滤子的扩张定理。

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