A short note on $L_{CBA}$ - fuzzy logic with a non-associative conjunction

• Autorzy: Miroslav Kolařík
• Języki publikacji: EN

Abstrakty

EN

We significantly simplify the axiomatic system $L_{CBA}$ for fuzzy logic with a non-associative conjunction.

Słowa kluczowe

EN

axiomatic system; non-associativity; fuzzy logic

Kategorie tematyczne

• 06F35: BCK-algebras, BCI-algebras
• 03G10: Lattices and related structures
• 06D35: MV-algebras

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2016
• Tom: 36
• Numer: 1
• Strony: 113-116

Daty

wydano

2016

otrzymano

2016-02-25

poprawiono

2016-03-10

Twórcy

autor

Miroslav Kolařík

• Palacký University Olomouc, Faculty of Science, Department of Computer Science, Třída 17. listopadu 12, 77146 Olomouc, Czech Republic

Bibliografia

• [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
• [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.
• [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
• [4] P. Hájek, Metamathematics of Fuzzy Logic, vol. 4 of Trends in Logic (Dordercht, Kluwer, 1998), 299 pages, ISBN 978-94-011-5300-3.
• [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
• [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
• [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] R.B. Nelsen, An Introduction to Copulas (Springer-Verlag, New York, 2006), 286 pages, ISBN 978-0-387-28659-4.
• [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
• [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

Identyfikatory

DOI

10.7151/dmgaa.1247