|本期目录/Table of Contents|

强Ockham代数与剩余格(PDF)

《纯粹数学与应用数学》[ISSN:1008-5513/CN:61-1240/O1]

期数:
2010年01期
页码:
123
栏目:
出版日期:
2010-01-15

文章信息/Info

Title:
Strong Ockham algebra and residuated lattice
作者:
张隆传 张小红
(宁波大学数学系, 浙江宁波315211)
Author(s):
ZHANG Long-chuan ZHANG Xiao-hong
(Department of Mathematics, Ningbo University, Ningbo 315211, China)
关键词:
模糊逻辑 强De Morgan 代数 Ockham 代数 剩余格 强Ockham 代数
Keywords:
fuzzy logic strong De Morgan algebras Ockham algebras residuated lattices strong Ockham algebras
分类号:
O153.1
DOI:
-
文献标识码:
A
摘要:
首先讨论了Ockham 代数与剩余格的关系, 引入了强Ockham 代数的概念, 并 讨论了它的基本性质. 然后, 将著名的R0 蕴涵和R0 算子推广到Ockham 代数上, 证 明了添加广义R0 蕴涵和广义R0 算子后的Ockham 代数L 成为剩余格的充要条件是 L 为强Ockham 代数. 最后给出若干重要例子, 以此来说明强Ockham 代数的条件是 独立的.
Abstract:
Firstly, the relation between Ockham algebras and residuated lattice are investigated, and the notion of Strong Ockham algebras is introduced, and its elementary properties are given. Secondly, the famous R0 implication and R0 operator are developed to Ockham algebras, which are called general R0 implication and general R0 operator. And the necessary and su±cient condition is proved as following: a Ockham algebra L with general R0 implication and general R0 operator becomes a Residuated lattice if and only if L is a Strong Ockham algebras. Finally, Some important examples are given to show that three conditions of Strong Ockham algebras are independent.

参考文献/References

-

备注/Memo

备注/Memo:
-
更新日期/Last Update: 2010-01-15