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山东大学学报（理学版） ›› 2016, Vol. 51 ›› Issue (4): 118-126.doi: 10.6040/j.issn.1671-9352.0.2015.275

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FI代数中基于相对非的滤子

吴苏朋1,2,赵彬1*   

  1. 1.陕西师范大学数学与信息科学学院, 陕西 西安 710062;2.安康学院数学与统计系, 陕西 安康 725000
  • 收稿日期:2015-06-08 出版日期:2016-04-20 发布日期:2016-04-08
  • 通讯作者: 赵彬(1965— ), 男, 博士, 教授, 研究方向为格上拓扑与模糊推理. E-mail:zhaobin@snnu.edu.cn E-mail:wusupeng@snnu.edu.cn
  • 作者简介:吴苏朋(1980— ), 女, 博士研究生, 讲师, 研究方向为模糊逻辑. E-mail:wusupeng@snnu.edu.cn
  • 基金资助:
    国家自然科学基金(11531009,11501343);中央高校基本科研业务费专项基金(GK201501001)

The filters based on relative negations in FI Algebras

WU Su-peng1,2, ZHAO Bin1*   

  1. 1. College of Mathematics and Information Science, Shaanxi Normal University, Xian 710062, Shaanxi, China;
    2. Department of Mathematics and Statistics, Ankang University, Ankang 725000, Shaanxi, China
  • Received:2015-06-08 Online:2016-04-20 Published:2016-04-08

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摘要： 引入了FI代数中相对非的概念, 讨论了相对非的性质。利用相对非给出了FI代数中相对正则滤子、扩展相对正则滤子和弱相对正则滤子的概念, 得到了这些滤子的特征定理。分析了FI代数中基于滤子的相对双补元之集的代数性质,得到了扩展相对正则滤子的应用。

关键词: 相对正则滤子, 扩展相对正则滤子, FI代数, 弱相对正则滤子

Abstract: The notion of relative negations in FI-algebras is proposed and some properties of it are discussed. Based on the relative negations, relative regular filters, extended relative regular filters and weak relative regular filters are defined, Some characteristic theorems of them are obtained. Algebraic properties of the set of relative double complemented elements based on the filters are introduced and the applications of extended relative regular filters are showd.

Key words: relative regular filter, weak relative regular filter, FI-algebra, extended relative regular filter

中图分类号: 

  • O141.1
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