BL-代数中的落影模糊理想

doi:10.6040/j.issn.1671-9352.0.2014.270

山东大学学报（理学版） ›› 2015, Vol. 50 ›› Issue (02): 83-89.doi: 10.6040/j.issn.1671-9352.0.2014.270

BL-代数中的落影模糊理想

杨永伟^1,2, 贺鹏飞², 李毅君²

1. 安阳师范学院数学与统计学院, 河南安阳 455000;
2. 西北大学数学学院, 陕西西安 710127

收稿日期:2014-06-16 修回日期:2014-10-15 出版日期:2015-02-20 发布日期:2015-01-27
作者简介:杨永伟 (1984-), 男, 博士, 讲师, 研究方向为模糊集理论、逻辑代数. E-mail:yangyw2010@126.com
基金资助:
陕西省教育厅科研计划项目(2013JK0562,14JK1535)

Falling fuzzy ideals of BL-algebras

YANG Yong-wei^1,2, HE Peng-fei², LI Yi-jun²

1. School of Mathematics and Statistics, Anyang Normal University, Anyang 455000, Henan, China;
2. School of Mathematics, Northwest University, Xi'an 710127, Shaanxi, China

Received:2014-06-16 Revised:2014-10-15 Online:2015-02-20 Published:2015-01-27

摘要/Abstract

摘要： 在落影理论的基础上,本文建立了定义BL-代数的模糊(关联)理想的理论方法.研究了落影模糊(关联)理想和模糊(关联)理想的关系,证明了模糊(关联)理想是落影模糊(关联)理想,反之不成立.最后,获得了落影模糊(关联)理想的一些等价刻画.

关键词: BL-代数, 模糊理想, 落影模糊理想, 落影模糊关联理想

Abstract: The paper establishes a theoretical approach to fuzzy (implicative) ideals of BL-algebras based on the theory of falling shadows. Then the relationships between falling fuzzy (implicative) ideals and fuzzy (implicative) ideals are investigated. It is proved that every fuzzy (implicative) ideal is a falling fuzzy (implicative) ideal, but not vice versa. Finally, some characterizations of falling fuzzy (implicative) ideals are obtained.

Key words: BL-algebra, fuzzy ideal, falling fuzzy ideal, falling fuzzy implicative ideal

中图分类号:

O159

杨永伟, 贺鹏飞, 李毅君. BL-代数中的落影模糊理想[J]. 山东大学学报（理学版）, 2015, 50(02): 83-89.

YANG Yong-wei, HE Peng-fei, LI Yi-jun. Falling fuzzy ideals of BL-algebras[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(02): 83-89.

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BL-代数中的落影模糊理想

Falling fuzzy ideals of BL-algebras

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