On fuzzy ideals in BCK/BCI-algebras

被引：28
|
作者：
Meng, J [1 ]
Guo, X
机构：
[1] NW Univ Xian, Dept Math, Xian 710069, Shaanxi, Peoples R China
[2] Fourth Mil Med Univ, Dept Hlth Stat, Xian 710033, Peoples R China
来源：
FUZZY SETS AND SYSTEMS | 2005年 / 149卷 / 03期
关键词：
BCK/BCI-algebra; fuzzy ideal; prime fuzzy ideal; fuzzy ideal lattice;
D O I：
10.1016/j.fss.2003.11.014
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
In the present paper we give a procedure by which we generate a fuzzy ideal (resp. closed fuzzy ideal) by a fuzzy set in a BCI-algebra. As applications we prove: The set of all the fuzzy ideals in a BCI-algebra forms a complete lattice (called fuzzy ideal lattice). The set of all the closed fuzzy ideals in a BCI-algebra is a modular sublattice of the fuzzy ideal lattice, but it is not distributive in general. For commutative BCK-algebras we establish the prime fuzzy ideal theorem. In particular, we give some characterizations of Noether BCK/BCI-algebras by fuzzy ideals. (C) 2003 Elsevier B.V. All rights reserved.
引用
收藏
页码：509 / 525
页数：17
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