FI代数的犹豫模糊滤子与犹豫模糊同余关系

Hesitant Fuzzy Filters and Hesitant Fuzzy Congruence Relationes in FI-algebras

将犹豫模糊集概念与FI代数的滤子和同余关系概念相结合，引入了FI代数的犹豫模糊滤子和犹豫模糊同余关系概念并研究它们的性质和相互关系．获得了FI代数在给定犹豫模糊同余关系下的商代数特征并建立了同态基本定理．证明了当分别在CFI代数的全体犹豫模糊滤子集和全体犹豫模糊同余关系集上定义适当的序关系后，二者保序同构．

In this paper, we combine hesitant congruence relation in FI-algebras. The notions fuzzy sets with the notions of filter and of hesitant fuzzy filter and hesitant fuzzy congruence relation are introduced, some their properties and relationships are investigated. The quotient algebra feature of an FI-algebra under a given hesitant fuzzy congruence relation is obtained, and the homomorphism fundamental theorem is established. It is proved that the set containing all of hesitant fuzzy filters and the set containing all of hesitant fuzzy congruence relations in a CFI-algebra is order preserving isomorphism, when proper order relations are defined on these two sets.