| 多值滤子及其应用 |
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| 引用本文： | 李令强,金秋.多值滤子及其应用[J].山东大学学报(理学版),2007,42(12):29-32. |
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| 作者姓名： | 李令强 金秋 |
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| 作者单位： | 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 |
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| 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.
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| 关 键 词： | 交换quantale Ω-强拓扑 Ω-滤子 |
| 文章编号： | 1671-9352（2007）12-0029-04 |
| 收稿时间： | 2007-06-05 |
| 修稿时间： | 2007年6月5日 |
Many-valued filter and its application |
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| LI Ling-qiang,QIU Jin.Many-valued filter and its application[J].Journal of Shandong University,2007,42(12):29-32. |
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| Authors: | LI Ling-qiang QIU Jin |
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| Institution: | 1. School of Mathematics Science， Sichuan University， Chengdu 610064, Sichuan, China；2. School of Mathematics Science, Linyi Normal University, Linyi 276005, Shandong， China |
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| 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. |
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| Keywords: | commutative quantale strong Ω-topology Ω-filter |
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