摘要
本文讨论了Ｆｕｚｙ格的Ｗ理想的一些基本性质。主要结果有：（１）对于一般的Ｆｕｚｙ格，给出了一个同余理想为Ｗ理想的若干充分条件和充要条件，所得结果是文［３］中相应结果在一般Ｆｕｚｙ格中的推广，从而完整地回答了文［３］中提出的一个问题；（２）对于Ｆｕｚｙ格下的同余素理想Ｐ，我们得到：Ｐ为Ｆ的Ｗ理想Ｆ／θ（Ｐ）为ＷＦｕｚｙ格；此时，Ｆ的的任一包含Ｐ的同余理想均为Ｗ理想。
In this paper some properties of W ideal in a Fuzzy lattice are discussed.First,for general Fuzzy lattices,we give some necessary or sufficient conditions for a congruence ideal to be a W ideal,those results generalize all results given in 3 .Next,we prove if P is a prime ideal of a Fuzzy lattice F then P is a W ideal of F iff F/θ(P) is a W Fuzzy lattice;and in this case any congruence ideal containing P is a W ideal of F.
出处
《模糊系统与数学》
CSCD
1997年第4期91-96,共6页
Fuzzy Systems and Mathematics
基金
国家自然科学基金
关键词
同余关系
同余理想
W-理想
W-模糊格
模糊格
,Fuzzy lattices
Congruence relations
Congruence ideals
W ideals
W Fuzzy latticesOn W Fuzzy Lattices and W Ideals Zhu Yiquan (Huanggang Teachers College,Huangzhou,436100) Pei Liwen (Whuan University,Wuhan,430072) ) Abstract In this paper some properties of W ideal in a Fuzzy lattice are discussed.First,for general Fuzzy lattices,we give some necessary or sufficient conditions for a congruence ideal to be a W ideal,those results generalize all results given in 3 .Next,we prove if P is a prime ideal of a Fuzzy lattice F then P is a W ideal of F iff F/θ(P) is a W Fuzzy lattice
and in this case any congruence ideal containing P is a W ideal of F. Keywords ,Fuzzy lattices
Congruence relations
Congruence ideals
W ideals
W Fuzzy lattices
