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山东大学学报（理学版） ›› 2016, Vol. 51 ›› Issue (2): 102-107.doi: 10.6040/j.issn.1671-9352.0.2015.116

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区间集上非交换剩余格的〈,(-overQ)〉-fuzzy滤子及其特征刻画

乔希民1,吴洪博2   

  1. 1.商洛学院数学与计算机应用学院, 陕西 商洛 726000;2.陕西师范大学数学与信息科学学院, 陕西 西安 710062
  • 收稿日期:2014-03-18 出版日期:2016-02-16 发布日期:2016-03-11
  • 作者简介:乔希民(1960— ),男,硕士,副教授,研究方向为非经典数理逻辑与格上拓扑学. E-mail:qiaoximin@163.com
  • 基金资助:
    国家自然科学基金资助项目(61572016);陕西省自然科学基础研究计划项目(2013JM1023);陕西省教育厅科研计划资助项目(11JK0512)

〈,(-overQ)〉-fuzzy filter and its characterization of the non-commutative residual lattices on the interval sets

QIAO Xi-min1, WU Hong-bo2   

  1. 1. School of Mathematics and Computer Application, Shangluo University, Shangluo 726000, Shaanxi, China;
    2. School of Mathematics and Information Science, Shaanxi Normal University, Xian 710062, Shaanxi, China
  • Received:2014-03-18 Online:2016-02-16 Published:2016-03-11

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摘要： 以区间集思想作为研究工具,讨论非交换剩余格和滤子理论,引入区间集上非交换剩余格与区间集上非交换剩余格fuzzy滤子的概念,给出区间集上非交换剩余格〈,(-overQ)〉-fuzzy滤子的代数结构,进一步得到若干等价性特征刻画,并对表示定理的充分必要条件予以证明。

关键词: 非可换模糊逻辑, 区间集上非交换剩余格, 区间集, 特征刻画, (-overQ)〉-fuzzy滤子, 〈

Abstract: Taking the thought of interval sets as the research tool, the theories of non-commutative residual lattices are discussed on the interval sets and filters. The concepts of non-commutative residual lattices are introduced on interval sets and fuzzy filters of non-commutative residual lattices on interval sets. The algebraic structure of the 〈,(-overQ)〉-fuzzy filters of non-commutative residual lattices is provided on interval sets, and several equivalent characterization are received. A detailed demonstration for the necessary and sufficient conditions of the representation theorem is given.

Key words: non-commutative fuzzy logic, non-commutative residual lattices on the interval sets, characterization, 〈,(-overQ)〉-fuzzy filters, interval sets

中图分类号: 

  • O141
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