Bounded commutative residuated l-monoids with general comparability and states

被引：20

作者：

Dvurecenskij, A

Rachunek, J

机构：

[1] Slovak Acad Sci, Inst Math, SK-81473 Bratislava, Slovakia

[2] Palacky Univ, Fac Sci, Dept Algebra & Geometry, CZ-77900 Olomouc, Czech Republic

来源：

SOFT COMPUTING | 2006年 / 10卷 / 03期

关键词：

bounded commutative Rl-monoid; general comparability property; Boolean element; State; State-morphism; extremal state; filter; maximal filter; MV-algebra; BL-algebra;

D O I：

10.1007/s00500-005-0473-0

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

Bounded commutative Rl-monoids are a generalization of MV-algebras as well as of BL-algebras. For such monoids the authors in [DvRa] introduced states, analogues of probability measures. We study Boolean elements and introduce the general comparability property. It entails that the monoids with the property are BL-algebras, and extremal states on Boolean elements can be uniquely extended to extremal states on the monoids. Moreover, the hull-kernel topology of maximal filters is totally disconnected.

引用

页码：212 / 218

页数：7

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