Interior and closure operators on bounded residuated lattices

• Autorzy: Jiří Rachůnek , Zdeněk Svoboda
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 06F05: Ordered semigroups and monoids
• 06A15: Galois correspondences, closure operators
• 03G10: Lattices and related structures
• 06D35: MV-algebras

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 3
• Strony: 534-544

Daty

wydano

2014-03-01

online

2013-12-21

Twórcy

autor

Jiří Rachůnek

• Palacký University

autor

Zdeněk Svoboda

• Palacký University

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-013-0349-y