# Interior and closure operators on bounded residuated lattices

Open Mathematics (2014)

- Volume: 12, Issue: 3, page 534-544
- ISSN: 2391-5455

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topJiří Rachůnek, and Zdeněk Svoboda. "Interior and closure operators on bounded residuated lattices." Open Mathematics 12.3 (2014): 534-544. <http://eudml.org/doc/269666>.

@article{JiříRachůnek2014,

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.},

author = {Jiří Rachůnek, Zdeněk Svoboda},

journal = {Open Mathematics},

keywords = {Residuated lattice; Bounded integral residuated lattice; Interior operator; Closure operator; residuated lattice; bounded integral residuated lattice; interior operator; closure operator},

language = {eng},

number = {3},

pages = {534-544},

title = {Interior and closure operators on bounded residuated lattices},

url = {http://eudml.org/doc/269666},

volume = {12},

year = {2014},

}

TY - JOUR

AU - Jiří Rachůnek

AU - Zdeněk Svoboda

TI - Interior and closure operators on bounded residuated lattices

JO - Open Mathematics

PY - 2014

VL - 12

IS - 3

SP - 534

EP - 544

AB - 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.

LA - eng

KW - Residuated lattice; Bounded integral residuated lattice; Interior operator; Closure operator; residuated lattice; bounded integral residuated lattice; interior operator; closure operator

UR - http://eudml.org/doc/269666

ER -

## References

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