Some properties of residuated lattices

Radim Bělohlávek

Czechoslovak Mathematical Journal (2003)

  • Volume: 53, Issue: 1, page 161-171
  • ISSN: 0011-4642

Abstract

top
We investigate some (universal algebraic) properties of residuated lattices—algebras which play the role of structures of truth values of various systems of fuzzy logic.

How to cite

top

Bělohlávek, Radim. "Some properties of residuated lattices." Czechoslovak Mathematical Journal 53.1 (2003): 161-171. <http://eudml.org/doc/30766>.

@article{Bělohlávek2003,
abstract = {We investigate some (universal algebraic) properties of residuated lattices—algebras which play the role of structures of truth values of various systems of fuzzy logic.},
author = {Bělohlávek, Radim},
journal = {Czechoslovak Mathematical Journal},
keywords = {residuated lattice; fuzzy logic; variety; congruence; residuated lattice; fuzzy logic; variety; congruence},
language = {eng},
number = {1},
pages = {161-171},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some properties of residuated lattices},
url = {http://eudml.org/doc/30766},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Bělohlávek, Radim
TI - Some properties of residuated lattices
JO - Czechoslovak Mathematical Journal
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 1
SP - 161
EP - 171
AB - We investigate some (universal algebraic) properties of residuated lattices—algebras which play the role of structures of truth values of various systems of fuzzy logic.
LA - eng
KW - residuated lattice; fuzzy logic; variety; congruence; residuated lattice; fuzzy logic; variety; congruence
UR - http://eudml.org/doc/30766
ER -

References

top
  1. 10.1007/s000120050194, Algebra Universalis 44 (2000), 375–377. (2000) MR1816031DOI10.1007/s000120050194
  2. Lattice Theory, 3rd ed. AMS Colloq. Publ., vol. XXV, Providence, Rhode Island, 1967. (1967) MR0227053
  3. Locally regular varieties, Acta Sci. Math. (Szeged) 64 (1998), 431–435. (1998) Zbl0913.08006MR1666006
  4. 10.1090/S0002-9947-1958-0094302-9, Trans. Amer. Math. Soc. 88 (1958), 467–490. (1958) Zbl0084.00704MR0094302DOI10.1090/S0002-9947-1958-0094302-9
  5. A new proof of completeness of the Łukasiewicz axioms, Trans. Amer. Math. Soc. 93 (1959), 74–90. (1959) MR0122718
  6. Algebraic Foundations of Many-valued Reasoning, Kluwer, Dordrecht, 1999. (1999) MR1786097
  7. 10.1007/s005000000044, Soft Computing 4 (2000), 106–112. (2000) DOI10.1007/s005000000044
  8. Characterizations of regular varieties, Acta Sci. Math. (Szeged) 31 (1970), 187–189. (1970) MR0272697
  9. 10.1090/S0002-9947-1939-1501995-3, Trans.  Amer. Math. Soc. 45 (1939), 335–354. (1939) MR1501995DOI10.1090/S0002-9947-1939-1501995-3
  10. Eine Bemerkung über Mannigfaltigkeiten universeller Algebren mit Idealen, Monatsb. Deutsch. Akad. Wiss. Berlin 12 (1970), 21–25. (1970) Zbl0198.33601MR0256968
  11. Wajsberg algebras, Stochastica 8 (1984), 5–31. (1984) MR0780136
  12. 10.1007/BF00485654, Synthese 19 (1968–69), 325–373. (1968–69) DOI10.1007/BF00485654
  13. Two Mal’cev-type theorems in universal algebra, J. Comb. Theory 8 (1970), 334–342. (1970) 
  14. Metamathematics of Fuzzy Logic, Kluwer, Dordrecht, 1998. (1998) MR1900263
  15. Commutative residuated monoids, In: Non-classical logics and their applications to fuzzy subsets, U. Höhle, E. P. Klement (eds.), Kluwer, Dordrecht, 1995. (1995) 
  16. 10.1006/jmaa.1996.0285, J.  Math. Anal. Appl. 201 (1996), 786–826. (1996) MR1400564DOI10.1006/jmaa.1996.0285
  17. On the representation of lattices, Math. Scand. 2 (1953), 295–314. (1953) 
  18. On the general theory of algebraic systems, Matem. Sbornik 35 (1954), 3–20. (Russian) (1954) 
  19. Mathematical Principles of Fuzzy Logic, Kluwer, Dordrecht, 1999. (1999) MR1733839
  20. On fuzzy logic  I, II, III, Zeit. Math. Log. Grungl. Math. 25 (1979), 45–52, 119–134, 447–464. (1979) MR0524558
  21. 10.1007/BF01236518, Algebra Universalis 31 (1994), 204–222. (1994) Zbl0799.08010MR1259350DOI10.1007/BF01236518
  22. Kongruenzklassengeometrien. Lecture Notes in Math, Springer-Verlag, Berlin-Heidelberg-New York, 1970. (1970) MR0262149

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.