On ⊙-Ideals and Lattices of ⊙-Ideals in Regular Residuated Lattices

被引：0
作者：
Liu, Chun-hui [1 ]
Xu, Luo-shan [1 ]
机构：
[1] Yangzhou Univ, Dept Math, Yangzhou 225002, Peoples R China
来源：
QUANTITATIVE LOGIC AND SOFT COMPUTING 2010, VOL 2 | 2010年 / 82卷
关键词：
Residuated lattice; circle dot-ideal; algebraic lattice; frame; FUZZY LOGIC; PROPOSITIONAL CALCULI; ALGEBRAS;
D O I：
暂无
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
In this paper, the operation circle dot and the concept of circle dot-ideals of (regular) residuated lattices are introduced. Some characterization theorems for circle dot-ideals of (regular) residuated lattices are given. Representation theorems about circle dot-ideals which are generated by non-empty subsets of regular residuated lattices are obtained. For the set of all circle dot-ideals of a (regular) residuated lattice, an adjunction pair is defined. It is proved that the lattice of all circle dot-ideals in a regular residuated lattice with the adjunction and the set-inclusion order is a complete Heyting algebra (i.e., a frame) and an algebraic lattice, which thus gives a new distributive residuated lattice.
引用
收藏
页码：425 / 434
页数：10
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