Interior and closure operators on bounded residuated lattices

被引：10

作者：

Rachunek, Jiri ^{[1
]}

Svoboda, Zdenek ^{[1
]}

机构：

[1] Palacky Univ, Fac Sci, Dept Algebra & Geometry, Olomouc 77146, Czech Republic

来源：

CENTRAL EUROPEAN JOURNAL OF MATHEMATICS | 2014年 / 12卷 / 03期

关键词：

Residuated lattice; Bounded integral residuated lattice; Interior operator; Closure operator;

D O I：

10.2478/s11533-013-0349-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Bounded integral residuated lattices form a large class of algebras containing some classes of algebras behind many valued and fuzzy logics. In the paper we introduce and investigate multiplicative interior and additive closure operators (mi- and ac-operators) generalizing topological interior and closure operators on such algebras. We describe connections between mi- and ac-operators, and for residuated lattices with Glivenko property we give connections between operators on them and on the residuated lattices of their regular elements.

引用

页码：534 / 544

页数：11