### Fuzzy filters and fuzzy congruence relations on residuated lattices

CHEN Juanjuan1，2, LI Shenggang1

1. 1.College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, China
2.Faculty of Sciences, Xi’an University of Technology, Xi’an 710048, China
• Online:2013-09-01 Published:2013-09-13

### 剩余格上的模糊滤子和模糊同余关系

1. 1.陕西师范大学 数学与信息科学学院，西安 710062
2.西安理工大学 理学院，西安 710048

Abstract: In this paper, it introduces definition of fuzzy filters and fuzzy congruence relations on residuated lattices, then it gives a one-to-one correspondence from the set of all fuzzy filters and the set of all fuzzy filters in residuated lattice. It is proved that an appropriate order relation can be defined on the set of all fuzzy filters （resp., the set of all fuzzy filters） such that they are complete lattice isomorphism.