A duality between algebras of basic logic and bounded representable D R l -monoids

Jiří Rachůnek

Mathematica Bohemica (2001)

  • Volume: 126, Issue: 3, page 561-569
  • ISSN: 0862-7959

Abstract

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B L -algebras, introduced by P. Hájek, form an algebraic counterpart of the basic fuzzy logic. In the paper it is shown that B L -algebras are the duals of bounded representable D R l -monoids. This duality enables us to describe some structure properties of B L -algebras.

How to cite

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Rachůnek, Jiří. "A duality between algebras of basic logic and bounded representable $DRl$-monoids." Mathematica Bohemica 126.3 (2001): 561-569. <http://eudml.org/doc/248688>.

@article{Rachůnek2001,
abstract = {$BL$-algebras, introduced by P. Hájek, form an algebraic counterpart of the basic fuzzy logic. In the paper it is shown that $BL$-algebras are the duals of bounded representable $DRl$-monoids. This duality enables us to describe some structure properties of $BL$-algebras.},
author = {Rachůnek, Jiří},
journal = {Mathematica Bohemica},
keywords = {$BL$-algebra; $MV$-algebra; bounded $DRl$-monoid; representable $DRl$-monoid; prime spectrum; basic fuzzy logic; BL-algebra; MV-algebra; bounded -monoid; representable -monoid; prime spectrum; basic fuzzy logic},
language = {eng},
number = {3},
pages = {561-569},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A duality between algebras of basic logic and bounded representable $DRl$-monoids},
url = {http://eudml.org/doc/248688},
volume = {126},
year = {2001},
}

TY - JOUR
AU - Rachůnek, Jiří
TI - A duality between algebras of basic logic and bounded representable $DRl$-monoids
JO - Mathematica Bohemica
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 126
IS - 3
SP - 561
EP - 569
AB - $BL$-algebras, introduced by P. Hájek, form an algebraic counterpart of the basic fuzzy logic. In the paper it is shown that $BL$-algebras are the duals of bounded representable $DRl$-monoids. This duality enables us to describe some structure properties of $BL$-algebras.
LA - eng
KW - $BL$-algebra; $MV$-algebra; bounded $DRl$-monoid; representable $DRl$-monoid; prime spectrum; basic fuzzy logic; BL-algebra; MV-algebra; bounded -monoid; representable -monoid; prime spectrum; basic fuzzy logic
UR - http://eudml.org/doc/248688
ER -

References

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Citations in EuDML Documents

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  1. Jan Kühr, Pseudo B L -algebras and D R ℓ -monoids
  2. Jiří Rachůnek, Vladimír Slezák, Negation in bounded commutative D R ℓ -monoids
  3. Jan Kühr, Spectral topologies of dually residuated lattice-ordered monoids
  4. Jiří Rachůnek, Dana Šalounová, Local bounded commutative residuated ℓ -monoids
  5. Jiří Rachůnek, Dana Šalounová, Classes of fuzzy filters of residuated lattice ordered monoids
  6. Jiří Rachůnek, Dana Šalounová, Lexicographic extensions of dually residuated lattice ordered monoids
  7. Jiří Rachůnek, Filip Švrček, Interior and closure operators on bounded commutative residuated l-monoids
  8. Jan Kühr, Representable dually residuated lattice-ordered monoids
  9. Filip Švrček, Interior and closure operators on bounded residuated lattice ordered monoids
  10. Jiří Rachůnek, Dana Šalounová, Classes of filters in generalizations of commutative fuzzy structures

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