多值滤子及其应用

多值滤子及其应用

李令强¹，金秋²

1．四川大学数学院，四川成都 610064； 2. 临沂师范学院数学系，山东临沂 276005

收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2006-10-24 发布日期:2006-10-24
通讯作者: 李令强

Many-valued filter and its application

LI Ling-qiang¹，QIU Jin²

1. School of Mathematics Science， Sichuan University， Chengdu 610064, Sichuan, China；2. School of Mathematics Science, Linyi Normal University, Linyi 276005, Shandong， China

Received:1900-01-01 Revised:1900-01-01 Online:2006-10-24 Published:2006-10-24
Contact: LI Ling-qiang

摘要/Abstract

摘要： 研究了模糊集理论中的一个基本问题：什么是多值滤子？利用模糊幂集固有的模糊偏序，通过给出滤子公理的多值解释，对该问题给出了一个新的回答.此外,作为多值滤子的一个应用,用它刻画了强Ω拓扑.

关键词: 交换quantale, Ω-滤子 , Ω-强拓扑

Abstract: A basic question in fuzzy set theory was studied: what is a many-valued filter on a set X? A new answer was presented by interpreting the axioms (three logical formulas) for classical filter theory in the fuzzy setting, which made use of the intrinsic fuzzy partial order on the fuzzy power set of X. The many valued filter theory was applied to characterize one of the many-valued topological theory —strong Ω-topology.

Key words: Ω-filter , strong Ω-topology, commutative quantale

中图分类号:

O159.1

李令强,金秋 . 多值滤子及其应用[J]. J4, 2007, 42(12): 29-32 .

LI Ling-qiang,QIU Jin . Many-valued filter and its application[J]. J4, 2007, 42(12): 29-32 .

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[1]	李令强, 李庆国. 格值模糊下近似算子的唯一公理刻画[J]. 山东大学学报（理学版）, 2014, 49(10): 78-82.
[2]	李令强金秋. Ω-滤子的一个等价刻画[J]. J4, 2009, 44(10): 51-53.
[3]	金秋,李令强 . L-模糊远域空间与L-余模糊拓扑空间[J]. J4, 2007, 42(9): 119-121 .