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山东大学学报（理学版） ›› 2018, Vol. 53 ›› Issue (2): 52-64.doi: 10.6040/j.issn.1671-9352.0.2017.403

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剩余格上的落影模糊滤子

彭家寅   

  1. 内江师范学院数学与信息科学学院, 四川 内江 641199
  • 收稿日期:2017-08-15 出版日期:2018-02-20 发布日期:2018-01-31
  • 作者简介:彭家寅(1962— ),男,博士,教授,研究方向为模糊数学与人工智能. E-mail:pengjiayin62226@163.con
  • 基金资助:
    教育部数学与应用数学专业综合改革项目(ZG0464);四川省科技厅重点科技项目(2006J13-035);四川省数学与成用数学专业综合改革项目(01249);国家自然科学基金资助项目(11071178);内江师范学院应用数学重点学科项目;四川省数学与应用数学专业卓越教师培养计划项目;内江师范学院卓越教师培养计划项目

Falling fuzzy filters on residuated lattices

PENG Jia-yin   

  1. School of Mathematics and Information Science, Neijiang Normal University, Neijiang 641199, Sichuan, China
  • Received:2017-08-15 Online:2018-02-20 Published:2018-01-31

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摘要： 利用落影理论重新建立剩余格的模糊滤子理论。 提出了剩余格的落影模糊滤子、落影模糊蕴涵滤子、落影模糊正蕴涵滤子、落影模糊Boolean、落影模糊G-滤子的概念,研究它们的相关性质。讨论了这些落影模糊滤子间的关系,获得了它们的一些等价刻画。给出了落影成为落影模糊滤子及落影模糊滤子成为模糊(正)蕴涵滤子的条件。探究了落影模糊(蕴涵、正蕴涵、Boolean、G-)滤子与模糊(蕴涵、正蕴涵、 Boolean、G-)滤子之间的关系。证明了在一定条件下,剩余格的落影模糊(G-)Boolean滤子与落影模糊(正)蕴涵滤子是等价的。

关键词: 落影模糊G-滤子, 剩余格, 落影模糊蕴涵滤子, 落影模糊正蕴涵滤子, 落影模糊Boolean滤子, 落影模糊滤子

Abstract: Using the theory of falling shadows, the fuzzy filter theory of residuated lattices is reestablished. The concepts of falling fuzzy filters, falling fuzzy implicative filters, falling fuzzy Boolean filters, falling fuzzy positive implicative filters and falling fuzzy G-filters on residuated lattices are introduced and their properties are investigated. The relations among them are discussed, and some equivalent characterizations of these filters are obtained. Conditions for a falling shadow to be a falling fuzzy filter, and for a falling fuzzy filter to be a falling fuzzy(positive)implicative filter are given. The relations between a falling fuzzy(implicative, positive implicative, Boolean, G-)filter and fuzzy(implicative, positive implicative, Boolean, G-)filter are studied. It is proved that falling fuzzy(G-)Boolean filter is equivalent to falling fuzzy(positive)implicative filter under certain conditions.

Key words: falling fuzzy filter, falling fuzzy implicative filter, falling fuzzy G-filter, falling fuzzy positive implicative filter, residatued lattice, falling fuzzy Boolean filter

中图分类号: 

  • TP18
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