A short note on L C B A - fuzzy logic with a non-associative conjunction

Miroslav Kolařík

Discussiones Mathematicae General Algebra and Applications (2016)

  • Volume: 36, Issue: 1, page 113-116
  • ISSN: 1509-9415

Abstract

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We significantly simplify the axiomatic system L C B A for fuzzy logic with a non-associative conjunction.

How to cite

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Miroslav Kolařík. "A short note on $L_{CBA}$ - fuzzy logic with a non-associative conjunction." Discussiones Mathematicae General Algebra and Applications 36.1 (2016): 113-116. <http://eudml.org/doc/286857>.

@article{MiroslavKolařík2016,
abstract = {We significantly simplify the axiomatic system $L_\{CBA\}$ for fuzzy logic with a non-associative conjunction.},
author = {Miroslav Kolařík},
journal = {Discussiones Mathematicae General Algebra and Applications},
keywords = {axiomatic system; non-associativity; fuzzy logic},
language = {eng},
number = {1},
pages = {113-116},
title = {A short note on $L_\{CBA\}$ - fuzzy logic with a non-associative conjunction},
url = {http://eudml.org/doc/286857},
volume = {36},
year = {2016},
}

TY - JOUR
AU - Miroslav Kolařík
TI - A short note on $L_{CBA}$ - fuzzy logic with a non-associative conjunction
JO - Discussiones Mathematicae General Algebra and Applications
PY - 2016
VL - 36
IS - 1
SP - 113
EP - 116
AB - We significantly simplify the axiomatic system $L_{CBA}$ for fuzzy logic with a non-associative conjunction.
LA - eng
KW - axiomatic system; non-associativity; fuzzy logic
UR - http://eudml.org/doc/286857
ER -

References

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  1. [1] M. Botur and R. Halaš, Commutative basic algebras and non-associative fuzzy logics, Arch. Math. Logic 48 (2009), 243-255. doi: 10.1007/s00153-009-0125-7 Zbl1168.03014
  2. [2] M. Botur, I. Chajda, R. Halaš, J. Kühr and J. Paseka, Algebraic Methods in Quantum Logic (Palacky University, Olomouc, 2014), 200 pages, ISBN 978-80-244-4166-5. Zbl1314.03003
  3. [3] P. Cintula, Short note: on the redundancy of axiom (A3) in BL and MTL, Soft Computing 9 (2005), 942-942. doi: 10.1007/s00500-004-0445-9 Zbl1093.03011
  4. [4] P. Hájek, Metamathematics of Fuzzy Logic, vol. 4 of Trends in Logic (Dordercht, Kluwer, 1998), 299 pages, ISBN 978-94-011-5300-3. Zbl0937.03030
  5. [5] P. Hájek and R. Mesiar, On copulas, quasicopulas and fuzzy logic, Soft Computing 12 (2008), 1239-1243. doi: 10.1007/s00500-008-0286-z Zbl1152.03018
  6. [6] V. Kreinovich, Towards more realistic (e.g. non-associative) 'and'- and 'or'-operations in fuzzy logic, Soft Computing 8 (2004), 274-280. doi: 10.1007/s00500-003-0272-4 Zbl1074.03011
  7. [7] S. Lehmke, Fun with automated proof search in basic propositional fuzzy logic, Abstracts of the Seventh International Conference FSTA 2004 (P.E. Klement, R. Mesiar, E. Drobná and F. Chovanec, eds.), (Liptovský Mikuláš), 2004, 78-80. 
  8. [8] R.B. Nelsen, An Introduction to Copulas (Springer-Verlag, New York, 2006), 286 pages, ISBN 978-0-387-28659-4. Zbl1152.62030
  9. [9] R.R. Yager, Modelling holistic fuzzy implication using co-copulas, Fuzzy Optim. Decis. Making 5 (2006), 207-226. doi: 10.1007/s10700-006-0011-2 Zbl1127.03324
  10. [10] H.H. Zimmerman and P. Zysno, Latent connectives in human decision making, Fuzzy Sets and Systems 4 (1980), 37-51. doi: 10.1016/0165-0114(80)90062-7 

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