# Sublattices corresponding to very true operators in commutative basic algebras

Discussiones Mathematicae - General Algebra and Applications (2014)

- Volume: 34, Issue: 2, page 183-189
- ISSN: 1509-9415

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topIvan Chajda, and Filip Švrček. "Sublattices corresponding to very true operators in commutative basic algebras." Discussiones Mathematicae - General Algebra and Applications 34.2 (2014): 183-189. <http://eudml.org/doc/270459>.

@article{IvanChajda2014,

abstract = {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.},

author = {Ivan Chajda, Filip Švrček},

journal = {Discussiones Mathematicae - General Algebra and Applications},

keywords = {commutative basic algebra; very true operator; idempotent operator; relatively complete sublattice},

language = {eng},

number = {2},

pages = {183-189},

title = {Sublattices corresponding to very true operators in commutative basic algebras},

url = {http://eudml.org/doc/270459},

volume = {34},

year = {2014},

}

TY - JOUR

AU - Ivan Chajda

AU - Filip Švrček

TI - Sublattices corresponding to very true operators in commutative basic algebras

JO - Discussiones Mathematicae - General Algebra and Applications

PY - 2014

VL - 34

IS - 2

SP - 183

EP - 189

AB - 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.

LA - eng

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

UR - http://eudml.org/doc/270459

ER -

## References

top- [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. Zbl1240.06043
- [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. Zbl1188.03048
- [3] I. Chajda, R. Halaš and J. Kühr, Distributive lattices with sectionally antitone involutions, Acta Sci. Math. (Szeged) 71 (2005) 19-33. Zbl1099.06006
- [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. Zbl0997.03028
- [6] L.A. Zadeh, A fuzzy-set-theoretical interpretation of linguistic hedges, J. Cybern. 2 (1972) 4-34.

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