L-fuzzy quantale 若干性质的研究

J4 ›› 2012, Vol. 47 ›› Issue (4): 104-109.

L-fuzzy quantale 若干性质的研究

梁少辉

西安科技大学理学院数学系, 陕西西安 710054

收稿日期:2011-04-01 出版日期:2012-04-20 发布日期:2012-06-28
作者简介:梁少辉(1981- ),男，博士，讲师，研究方向为格上拓扑与模糊推理. Email: liangshaohui1011@163.com
基金资助:
西安科技大学培育基金资助项目(2010041);西安科技大学博士基金资助项目(2010QDJ024)

Researches on some properties of L-fuzzy quantale

LIANG Shao-hui

Department of Mathematics, Xi’an University of Science and Technology, Xi’an 710054, Shaanxi, China

Received:2011-04-01 Online:2012-04-20 Published:2012-06-28

摘要/Abstract

摘要：

首先给出了L-fuzzy quantale的定义,将L-fuzzy frame的一些重要结论推广到L-fuzzy quantale中, 并给出了L-fuzzy quantale的一些等价刻画。其次,在Quantale中引入了L-滤子以及L-滤子Quantale的概念,证明了由任意一个L-滤子可以生成一个L-fuzzy quantale,在范畴L-FilQuant 与范畴L-FQuant之间可以建立一个诚实函子。最后,引入了L-fuzzy理想、准素理想以及素理想的概念,讨论了它们的一些性质,得到了若干重要结论。

关键词: L-fuzzy quantale; L-滤子; 范畴; 函子; 理想

Abstract:

The definition of L-fuzzy frame is generalized to L-fuzzy quantale, and some equivalent charaterizations of L-fuzzy quantale are given. The concept of L-filter and L-filtered quantale are introduced. It is proved that every L-filter can generate an L-filtered quantale, and there is an honest functor from L-FilQuant to L-FQuant. Finally, the concept of L-fuzzy ideal and L-fuzzy prime ideal are introduced, and their properties are discussed.

Key words: L-fuzzy quantale; L-filter; category; functor; ideal

梁少辉. L-fuzzy quantale 若干性质的研究[J]. J4, 2012, 47(4): 104-109.

LIANG Shao-hui. Researches on some properties of L-fuzzy quantale[J]. J4, 2012, 47(4): 104-109.

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