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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.
Kategorie tematyczne
Rocznik
Tom
Numer
Strony
183-189
Opis fizyczny
Daty
wydano
2014
otrzymano
2014-03-31
poprawiono
2014-07-17
Twórcy
autor
- Department of Algebra and Geometry, Palacký University Olomouc, 17. listopadu 12, 771 46 Olomouc, Czech Republic
autor
- 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.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1220