Interior and Closure Operators on Commutative Bounded Residuated Lattices

Jiří Rachůnek; Zdeněk Svoboda

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2013)

  • Volume: 52, Issue: 1, page 121-134
  • ISSN: 0231-9721

Abstract

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Commutative 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 additive closure and multiplicative interior operators on this class of algebras.

How to cite

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Rachůnek, Jiří, and Svoboda, Zdeněk. "Interior and Closure Operators on Commutative Bounded Residuated Lattices." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 52.1 (2013): 121-134. <http://eudml.org/doc/260702>.

@article{Rachůnek2013,
abstract = {Commutative 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 additive closure and multiplicative interior operators on this class of algebras.},
author = {Rachůnek, Jiří, Svoboda, Zdeněk},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {residuated lattice; bounded integral residuated lattice; interior operator; closure operator; residuated lattice; bounded integral residuated lattice; interior operator; closure operator},
language = {eng},
number = {1},
pages = {121-134},
publisher = {Palacký University Olomouc},
title = {Interior and Closure Operators on Commutative Bounded Residuated Lattices},
url = {http://eudml.org/doc/260702},
volume = {52},
year = {2013},
}

TY - JOUR
AU - Rachůnek, Jiří
AU - Svoboda, Zdeněk
TI - Interior and Closure Operators on Commutative Bounded Residuated Lattices
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2013
PB - Palacký University Olomouc
VL - 52
IS - 1
SP - 121
EP - 134
AB - Commutative 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 additive closure and multiplicative interior operators on this class of algebras.
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/260702
ER -

References

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  2. Cignoli, R. L. O., D’Ottaviano, M. L., Mundici, D., Algebraic Foundations of Many-valued Reasoning, Kluwer Academic Publishers, Dordrecht, 2000. (2000) MR1786097
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  9. Hájek, P., Metamathematics of Fuzzy Logic, Springer, Dordrecht, 1998. (1998) MR1900263
  10. Jipsen, P., Montagna, A., 10.1007/s00012-009-2106-4, Algebra Universalis 60 (2009), 381–404. (2009) Zbl1192.06011MR2504748DOI10.1007/s00012-009-2106-4
  11. Jipsen, P., Tsinakis, C., A Survey of Residuated Lattices, In: Ordered Algebraic Structures, Kluwer, Dordrecht, (2006), 19–56. (2006) MR2083033
  12. Rachůnek, J., Slezák, V., 10.1007/s10587-006-0053-1, Czechoslovak Math. J. 56 (2007), 755–763. (2007) DOI10.1007/s10587-006-0053-1
  13. Rachůnek, J., Švrček, F., MV-algebras with additive closure operators, Acta Univ. Palacki. Olomouc., Fac. Rer. Nat., Math. 39 (2000), 183–189. (2000) Zbl1039.06005MR1826361
  14. Rachůnek, J., Švrček, F., 10.7151/dmgaa.1132, Discuss. Math., Gen. Alg. Appl. 28 (2008), 11–27. (2008) Zbl1227.06014MR2437765DOI10.7151/dmgaa.1132
  15. Sikorski, R., Boolean Algebras, 2nd edition, Springer-Verlag, Berlin–Göttingen–Heidelbeg–New York, 1963. (1963) Zbl0122.26101

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