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高校应用数学学报
高校应用数学学报  2016, Vol. 31 Issue (2): 233-247    
    
剩余格的模糊滤子理论
刘春辉
赤峰学院 数学与统计学院, 内蒙古赤峰 024001
Fuzzy filters theory of residuated lattices
LIU Chun-hui
Department of Mathematics and Statistics, Chifeng University, Chifeng 024001, China
 全文: PDF 
摘要： 运用模糊集的方法和原理进一步深入研究剩余格的滤子问题. 在剩余格中引入了模糊预线性滤子, 模糊可除滤子和模糊Glivenko滤子三类新的模糊滤子概念, 给出了它们的若干性质和等价刻画. 系统讨论了这三类模糊滤子以及模糊正关联滤子,模糊Boolean滤子, 模糊MV滤子和模糊正则滤子间的相互关系, 证明了一个模糊滤子为模糊MV滤子当且仅当它既是模糊正则滤子又是模糊可除滤子的结论.
关键词： 剩余格;  模糊滤子;  模糊预线性滤子;  模糊可除滤子;  模糊Glivenko滤子    
Abstract: The problem of fuzzy filters in residuated lattices is deeply studied by using the principle and method of fuzzy sets. Three new notions of fuzzy prelinear, divisible and Glivenko filters are introduced in residuated lattices. Some of their properties and characterizations are given. Relations among these new fuzzy filters, fuzzy positive implicative filter, fuzzy Boolean filter, fuzzy MV filter, and fuzzy regular filter are discussed systematically. It is proved that a fuzzy filter is a fuzzy MV filter if and only if it is both a fuzzy regular filter and a fuzzy divisible filter.
Key words: residuated lattice    fuzzy filter    fuzzy prelinear filter    fuzzy divisible filter    fuzzy Glivenko filter
收稿日期: 2015-05-18 出版日期: 2018-05-17
CLC:  O141.1  
基金资助: 内蒙古自治区高等学校科学研究项目(NJSY14283)
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引用本文:

刘春辉. 剩余格的模糊滤子理论[J]. 高校应用数学学报, 2016, 31(2): 233-247.

LIU Chun-hui. Fuzzy filters theory of residuated lattices. Applied Mathematics A Journal of Chinese Universities, 2016, 31(2): 233-247.

链接本文:

http://www.zjujournals.com/amjcua/CN/    或    http://www.zjujournals.com/amjcua/CN/Y2016/V31/I2/233

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