Classes of filters in generalizations of commutative fuzzy structures

Jiří Rachůnek; Dana Šalounová

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2009)

  • Volume: 48, Issue: 1, page 93-107
  • ISSN: 0231-9721

Abstract

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Bounded commutative residuated lattice ordered monoids ( R ℓ -monoids) are a common generalization of 𝐵𝐿 -algebras and Heyting algebras, i.e. algebras of basic fuzzy logic and intuitionistic logic, respectively. In the paper we develop the theory of filters of bounded commutative R ℓ -monoids.

How to cite

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Rachůnek, Jiří, and Šalounová, Dana. "Classes of filters in generalizations of commutative fuzzy structures." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 48.1 (2009): 93-107. <http://eudml.org/doc/35184>.

@article{Rachůnek2009,
abstract = {Bounded commutative residuated lattice ordered monoids ($R\ell $-monoids) are a common generalization of $\mathit \{BL\}$-algebras and Heyting algebras, i.e. algebras of basic fuzzy logic and intuitionistic logic, respectively. In the paper we develop the theory of filters of bounded commutative $R\ell $-monoids.},
author = {Rachůnek, Jiří, Šalounová, Dana},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Residuated $\ell $-monoid; deductive system; $\mathit \{BL\}$-algebra; $\mathit \{MV\}$-algebra; Heyting algebra; filter; residuated lattice-ordered monoids; residuated -monoid; deductive system; BL-algebra; MV-algebra; Heyting algebra; filter},
language = {eng},
number = {1},
pages = {93-107},
publisher = {Palacký University Olomouc},
title = {Classes of filters in generalizations of commutative fuzzy structures},
url = {http://eudml.org/doc/35184},
volume = {48},
year = {2009},
}

TY - JOUR
AU - Rachůnek, Jiří
AU - Šalounová, Dana
TI - Classes of filters in generalizations of commutative fuzzy structures
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2009
PB - Palacký University Olomouc
VL - 48
IS - 1
SP - 93
EP - 107
AB - Bounded commutative residuated lattice ordered monoids ($R\ell $-monoids) are a common generalization of $\mathit {BL}$-algebras and Heyting algebras, i.e. algebras of basic fuzzy logic and intuitionistic logic, respectively. In the paper we develop the theory of filters of bounded commutative $R\ell $-monoids.
LA - eng
KW - Residuated $\ell $-monoid; deductive system; $\mathit {BL}$-algebra; $\mathit {MV}$-algebra; Heyting algebra; filter; residuated lattice-ordered monoids; residuated -monoid; deductive system; BL-algebra; MV-algebra; Heyting algebra; filter
UR - http://eudml.org/doc/35184
ER -

References

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  14. Rachůnek, J., Šalounová, D., Boolean deductive systems of bounded commutative residuated ℓ -monoids, Contrib. Gen. Algebra 16 (2005), 199–208. (2005) Zbl1081.06014
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