Sublattices corresponding to very true operators in commutative basic algebras

• Autorzy: Ivan Chajda , Filip Švrček
• Języki publikacji: EN

Abstrakty

EN

We introduce the concept of very true operator on a commutative basic algebra in a way analogous to that for fuzzy logics. We are motivated by the fact that commutative basic algebras form an algebraic axiomatization of certain non-associative fuzzy logics. We prove that every such operator is fully determined by a certain relatively complete sublattice provided its idempotency is assumed.

Słowa kluczowe

EN

commutative basic algebra; very true operator; idempotent operator; relatively complete sublattice

Kategorie tematyczne

• 06B23: Complete lattices, completions
• 03B45: Modal logic (including the logic of norms)
• 03G25: Other algebras related to logic

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2014
• Tom: 34
• Numer: 2
• Strony: 183-189

Daty

wydano

2014

otrzymano

2014-03-31

poprawiono

2014-07-17

Twórcy

autor

Ivan Chajda

• Department of Algebra and Geometry, Palacký University Olomouc, 17. listopadu 12, 771 46 Olomouc, Czech Republic

autor

Filip Švrček

• Department of Algebra and Geometry, Palacký University Olomouc, 17. listopadu 12, 771 46 Olomouc, Czech Republic

Bibliografia

• [1] M. Botur and F. Švrček, Very true on CBA fuzzy logic, Math. Slovaca 60 (2010) 435-446. doi: 10.2478/s12175-010-0023-9.
• [2] M. Botur, I. Chajda and R. Halaš, Are basic algebras residuated lattices?, Soft Comp. 14 (2010) 251-255. doi: 10.1007/s00500-009-0399-z.
• [3] I. Chajda, R. Halaš and J. Kühr, Distributive lattices with sectionally antitone involutions, Acta Sci. Math. (Szeged) 71 (2005) 19-33.
• [4] I. Chajda, R. Halaš and J. Kühr, Semilattice Structures (Heldermann Verlag (Lemgo, Germany), 2007).
• [5] P. Hájek, On very true, Fuzzy Sets and Systems 124 (2001) 329-333.
• [6] L.A. Zadeh, A fuzzy-set-theoretical interpretation of linguistic hedges, J. Cybern. 2 (1972) 4-34.

Identyfikatory

DOI

10.7151/dmgaa.1220