Fuzzy filters and fuzzy congruence relations on residuated lattices

Computer Engineering and Applications ›› 2013, Vol. 49 ›› Issue (17): 12-14.

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Fuzzy filters and fuzzy congruence relations on residuated lattices

CHEN Juanjuan1，2, LI Shenggang1

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

陈娟娟1，2，李生刚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

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.

Key words: residuated lattice, fuzzy filter, fuzzy congruence relation

摘要： 介绍了剩余格上的模糊同余关系和模糊滤子的定义，给出了剩余格上模糊滤子和模糊同余关系间的一一对应，证明了在剩余格上模糊滤子和模糊同余关系上定义适当的序关系可使它们是完备格同构。

关键词: 剩余格, 模糊滤子, 模糊同余关系

CHEN Juanjuan1，2, LI Shenggang1. Fuzzy filters and fuzzy congruence relations on residuated lattices[J]. Computer Engineering and Applications, 2013, 49(17): 12-14.

陈娟娟1，2，李生刚1. 剩余格上的模糊滤子和模糊同余关系[J]. 计算机工程与应用, 2013, 49(17): 12-14.

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Fuzzy filters and fuzzy congruence relations on residuated lattices

剩余格上的模糊滤子和模糊同余关系

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