Bounded dually residuated lattice ordered monoids as a generalization of fuzzy structures

Jiří Rachůnek; Vladimír Slezák

Mathematica Slovaca (2006)

  • Volume: 56, Issue: 2, page 223-233
  • ISSN: 0139-9918

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Rachůnek, Jiří, and Slezák, Vladimír. "Bounded dually residuated lattice ordered monoids as a generalization of fuzzy structures." Mathematica Slovaca 56.2 (2006): 223-233. <http://eudml.org/doc/32379>.

@article{Rachůnek2006,
author = {Rachůnek, Jiří, Slezák, Vladimír},
journal = {Mathematica Slovaca},
keywords = {residuated lattices; fuzzy logic},
language = {eng},
number = {2},
pages = {223-233},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Bounded dually residuated lattice ordered monoids as a generalization of fuzzy structures},
url = {http://eudml.org/doc/32379},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Rachůnek, Jiří
AU - Slezák, Vladimír
TI - Bounded dually residuated lattice ordered monoids as a generalization of fuzzy structures
JO - Mathematica Slovaca
PY - 2006
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 56
IS - 2
SP - 223
EP - 233
LA - eng
KW - residuated lattices; fuzzy logic
UR - http://eudml.org/doc/32379
ER -

References

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  2. CIGNOLI R. L. O.-D'OTTAVIANO I. M. L.-MUNDICI D., Algebraic Foundations of Many-Valued Reasoning, Kluwer Acad. Publ., Dordrecht-Boston-London, 2000. Zbl0937.06009MR1786097
  3. CIGNOLI R.-TORRENS A., Hájek basic fuzzy logic and Lukasiewicz infinite valued logic, Arch. Math. Logic 42 (2003), 361-370. Zbl1025.03018MR2018087
  4. DI NOLA A.-GEORGESCU G.-IORGULESCU A., Pseudo BL-algebras I, Mult.-Valued Log. 8 (2002), 673-714. Zbl1028.06007MR1948853
  5. DI NOLA A.-GEORGESCU G.-IORGULESCU A., Pseudo BL-algebras II, Mult.-Valued Log. 8 (2002), 715-750. Zbl1028.06008MR1948854
  6. DVUREČENSKIJ A.-PULMANNOVÁ S., New Trends in Quantum Structures, Kluwer Acad. Publ./Ister Science, Dordrecht/Bratislava, 2000. Zbl0987.81005MR1861369
  7. GEORGESCU G., Bosbach states on fuzzy structures, Soft Comput. 8 (2004), 217-230. Zbl1081.06012
  8. GEORGESCU G.-IORGULESCU A., Pseudo MV-algebras, Mult.-Valued Log. 6 (2001), 95-135. Zbl1014.06008MR1817439
  9. HÁJEK P., Metamathematics of Fuzzy Logic, Kluwer Acad. Publ., Amsterdam, 1998. (1998) Zbl0937.03030MR1900263
  10. HÁJEK P., Fuzzy logics with non-commutative conjunction, J. Logic Comput. 13 (2003), 469 479. MR1999959
  11. KOVÁŘ T., A General Theory of Dually Residuated Lattice Ordered Monoids, Ph.D. Thesis, Palacky Univ., Olomouc, 1996. (1996) 
  12. KÜHR J., Pseudo BL-algebras and DRI-monoids, Math. Bohem. 128 (2003), 199-208. MR1995573
  13. KÜHR J., Dually Residuated Lattice Ordered Monoids, Ph.D. Thesis, Palacky Univ., Olomouc, 2003. Zbl1141.06014
  14. LAMBEK J., Some lattice models of bilinear logic, Algebra Universalis 34 (1995), 541-550. (1995) Zbl0840.03044MR1357483
  15. RACHŮNEK J., A non-commutative generalization of MV-algebras, Czechoslovak Math. J. 52 (2002), 255-273. Zbl1012.06012MR1905434
  16. RACHŮNEK J., Prime spectra of non-commutative generalizations of MV-algebras, Algebra Universalis 48 (2002), 151-169. Zbl1058.06015MR1929902
  17. RACHŮNEK J.-SLEZÁK V., Negation in bounded commutative DRI-monoids, Czechoslovak Math. J. (To appear). MR2291772
  18. SWAMY K. L. N., Dually residuated lattice ordered semigroups, Math. Ann. 159 (1965), 105-114. (1965) Zbl0138.02104MR0183797

Citations in EuDML Documents

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  1. Anatolij Dvurečenskij, Jiří Rachůnek, On Riečan and Bosbach states for bounded non-commutative R ℓ -monoids
  2. Jiří Rachůnek, Dana Šalounová, Local bounded commutative residuated ℓ -monoids
  3. Jiří Rachůnek, Zdeněk Svoboda, Monotone modal operators on bounded integral residuated lattices
  4. Filip Švrček, Interior and closure operators on bounded residuated lattice ordered monoids
  5. Jiří Rachůnek, Dana Šalounová, Classes of filters in generalizations of commutative fuzzy structures
  6. Jiří Rachůnek, Dana Šalounová, Modal operators on bounded residuated l -monoids

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