摘要: Application of hesitant fuzzy sets to filter theory of Heyting algebras is discussed. The notion of hesitant fuzzy ( Boolean, implicative，positive implicative, ultra, obstinate ) filter of Heyting algebras is introduced, and related properties are investigated. Characterizations of hesitant fuzzy ( Boolean, implicative, positive implicative, ultra，obstinate ) filters of Heyting algebras are derived. Conditions for a hesitant fuzzy set to be a hesitant fuzzy filter are investigated. the equivalent relation between a hesitant fuzzy ( Boolean) filter and a hesitant fuzzy (implicative) positive implicative filter is given. The extension properties for hesitant fuzzy Boolean filter, hesitant fuzzy ultra filter and hesitant fuzzy obstinate filter are established. Finally, it is proved that the homomorphic preimage of a hesitant fuzzy ( Boolean, implicative, positive implicative, ultra, obstinate ) filter is also a hesitant fuzzy ( Boolean, implicative，positive implicative， ultra， obstinate ) filter.