正则剩余格的fuzzy⊙理想

J4 ›› 2010, Vol. 45 ›› Issue (10): 66-70.

正则剩余格的fuzzy⊙理想

秦学成, 刘春辉*

赤峰学院初等教育学院, 内蒙古赤峰 024001

收稿日期:2009-08-27 出版日期:2010-10-16 发布日期:2010-10-19
通讯作者: 刘春辉(1982-),男,硕士,讲师,研究方向为非经典数理逻辑.
作者简介:秦学成 (1963-),男,副教授,研究方向为计算机代数. Email: cfxyqinxuecheng@yahoo.com.cn

Fuzzy ⊙-ideals in regular residuated lattices

QIN Xue-cheng, LIU Chun-hui*

College of Elementary Education, Chifeng University, Chifeng 024001, Inner Mongolia, China

Received:2009-08-27 Online:2010-10-16 Published:2010-10-19

摘要/Abstract

摘要：

剩余格在模糊逻辑的研究中扮演着一个重要的角色。首先在剩余格中引入fuzzy⊙理想的概念, 讨论了(正则)剩余格中fuzzy⊙理想性质, 给出了正则剩余格中fuzzy⊙理想的若干等价刻画。其次, 利用fuzzy⊙理想概念构造了一个同余关系, 证明一个正则剩余格在该同余关系下的商代数还是正则剩余格。

关键词: 模糊逻辑;(正则)剩余格;fuzzy⊙理想; 同余关系;商代数

Abstract:

Residuated lattices play an important role in studies of fuzzy logic. First, the notions of fuzzy ⊙-ideals in residuated lattices are introduced. Some properties of fuzzy ⊙-ideals in (regular)residuated lattices are discussed and some equivalent characterizations are given. Second, a congruence relation is structured in terms of the notion of fuzzy ⊙-ideal in regular residuated lattices. It is proved that the quotient algebra of a regular residuated lattice under a congruence relation is also a regular residuated lattice.

Key words: fuzzy logic; (regular)residuated lattices; fuzzy ⊙-ideals; congruence relation; quotient algebra

秦学成, 刘春辉*. 正则剩余格的fuzzy⊙理想[J]. J4, 2010, 45(10): 66-70.

QIN Xue-cheng, LIU Chun-hui*. Fuzzy ⊙-ideals in regular residuated lattices[J]. J4, 2010, 45(10): 66-70.

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