Quantic格的模糊理想

J4 ›› 2013, Vol. 48 ›› Issue (10): 99-104.

Quantic格的模糊理想

周欣，赵彬*

陕西师范大学数学与信息科学学院, 陕西西安 710062

收稿日期:2013-01-17 发布日期:2013-10-14
通讯作者: 赵彬(1965- ),男,教授,博士生导师,研究方向为格上拓扑与模糊推理.Email: zhaobin@snnu.edu.cn
作者简介:周欣(1986- ),女,博士,研究方向为格上拓扑与模糊推理.Email: sxxzx1986@163.com
基金资助:
国家自然科学基金资助项目(11171196,11301316); 中央高校基本科研业务费专项基金项目(GK201302003)

Fuzzy ideals in Quantic lattices

ZHOU Xin, ZHAO Bin*

College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, Shaanxi, China

Received:2013-01-17 Published:2013-10-14

摘要/Abstract

摘要：

引入Quantic格上的模糊子Quantic格、模糊理想和素模糊理想的概念, 研究了模糊理想和素模糊理想的若干性质。讨论了Quantic格模糊理想与模糊子Quantic格之间的关系, 给出了模糊理想和素模糊理想的刻画, 证明了Quantic格的任意一个理想都可看成是此Quantic格的某一模糊理想的一个截集。

关键词: Quantic格; 模糊子Quantic格; 模糊理想; 素模糊理想

Abstract:

The concepts of fuzzy subquantic lattices, fuzzy ideals and prime fuzzy ideals of a quantic lattice are given. Then the relationships between fuzzy ideals and fuzzy subquantic lattices are discussed and the characterizations of fuzzy ideals and prime fuzzy ideals are studied. It is proved that every ideal of a quantic lattice can be regarded as a cutset of a fuzzy ideal.

Key words: Quantic lattice; fuzzy subquantic lattice; fuzzy ideal; prime fuzzy ideal

中图分类号:

O153.1

周欣，赵彬*. Quantic格的模糊理想[J]. J4, 2013, 48(10): 99-104.

ZHOU Xin, ZHAO Bin*. Fuzzy ideals in Quantic lattices[J]. J4, 2013, 48(10): 99-104.

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