Heyting代数的犹豫模糊滤子

Hesitant Fuzzy Filters of Heyting Algebras

讨论了犹豫模糊集在Heyting代数滤子理论中的应用,引入了Heyting代数的犹豫模糊(布尔、蕴涵、正蕴涵、超、顽固)滤子的概念,并研究了相关性质.给出了Heyting代数的犹豫模糊(布尔、蕴涵、正蕴涵、超、顽固)滤子的特征,研究了一个犹豫模糊集成为一个犹豫模糊滤子的条件.给出了犹豫模糊(布尔)滤子与犹豫模糊(蕴涵)正蕴涵滤子之间的等价关系,建立了犹豫模糊布尔滤子、犹豫模糊超滤子和犹豫模糊顽固滤子的扩展性质.最后,证明了犹豫模糊(布尔、蕴涵、正蕴涵、超、顽固)滤子的同态原象也是一个犹豫模糊(布尔、蕴涵、正蕴涵、超、顽固)滤子.

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.