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Interior and closure operators on bounded residuated lattices

✍ Scribed by Rachůnek, Jiří ;Svoboda, Zdeněk

Book ID: 121586240
Publisher: Walter de Gruyter GmbH
Year: 2014
Tongue: English
Weight: 859 KB
Volume: 12
Category: Article
ISSN: 2391-5455
DOI: 10.2478/s11533-013-0349-y

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✦ Synopsis

Abstract

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.

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