Classes of fuzzy filters of residuated lattice ordered monoids

Jiří Rachůnek; Dana Šalounová

Mathematica Bohemica (2010)

  • Volume: 135, Issue: 1, page 81-97
  • ISSN: 0862-7959

Abstract

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The logical foundations of processes handling uncertainty in information use some classes of algebras as algebraic semantics. Bounded residuated lattice ordered monoids (monoids) are common generalizations of BL -algebras, i.e., algebras of the propositional basic fuzzy logic, and Heyting algebras, i.e., algebras of the propositional intuitionistic logic. From the point of view of uncertain information, sets of provable formulas in inference systems could be described by fuzzy filters of the corresponding algebras. In the paper we investigate implicative, positive implicative, Boolean and fantastic fuzzy filters of bounded Rl -monoids.

How to cite

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Rachůnek, Jiří, and Šalounová, Dana. "Classes of fuzzy filters of residuated lattice ordered monoids." Mathematica Bohemica 135.1 (2010): 81-97. <http://eudml.org/doc/38113>.

@article{Rachůnek2010,
abstract = {The logical foundations of processes handling uncertainty in information use some classes of algebras as algebraic semantics. Bounded residuated lattice ordered monoids (monoids) are common generalizations of $\text\{\rm BL\}$-algebras, i.e., algebras of the propositional basic fuzzy logic, and Heyting algebras, i.e., algebras of the propositional intuitionistic logic. From the point of view of uncertain information, sets of provable formulas in inference systems could be described by fuzzy filters of the corresponding algebras. In the paper we investigate implicative, positive implicative, Boolean and fantastic fuzzy filters of bounded $\text\{\rm Rl\}$-monoids.},
author = {Rachůnek, Jiří, Šalounová, Dana},
journal = {Mathematica Bohemica},
keywords = {residuated $\text\{\rm l\}$-monoid; non-classical logics; basic fuzzy logic; intuitionistic logic; filter; fuzzy filter; $\text\{\rm BL\}$-algebra; $\text\{\rm MV\}$-algebra; Heyting algebra; residuated -monoid; fuzzy filter; BL-algebra; MV-algebra; Heyting algebra},
language = {eng},
number = {1},
pages = {81-97},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Classes of fuzzy filters of residuated lattice ordered monoids},
url = {http://eudml.org/doc/38113},
volume = {135},
year = {2010},
}

TY - JOUR
AU - Rachůnek, Jiří
AU - Šalounová, Dana
TI - Classes of fuzzy filters of residuated lattice ordered monoids
JO - Mathematica Bohemica
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 135
IS - 1
SP - 81
EP - 97
AB - The logical foundations of processes handling uncertainty in information use some classes of algebras as algebraic semantics. Bounded residuated lattice ordered monoids (monoids) are common generalizations of $\text{\rm BL}$-algebras, i.e., algebras of the propositional basic fuzzy logic, and Heyting algebras, i.e., algebras of the propositional intuitionistic logic. From the point of view of uncertain information, sets of provable formulas in inference systems could be described by fuzzy filters of the corresponding algebras. In the paper we investigate implicative, positive implicative, Boolean and fantastic fuzzy filters of bounded $\text{\rm Rl}$-monoids.
LA - eng
KW - residuated $\text{\rm l}$-monoid; non-classical logics; basic fuzzy logic; intuitionistic logic; filter; fuzzy filter; $\text{\rm BL}$-algebra; $\text{\rm MV}$-algebra; Heyting algebra; residuated -monoid; fuzzy filter; BL-algebra; MV-algebra; Heyting algebra
UR - http://eudml.org/doc/38113
ER -

References

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