Sublattices corresponding to very true operators in commutative basic algebras

Ivan Chajda; Filip Švrček

Discussiones Mathematicae - General Algebra and Applications (2014)

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

Abstract

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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.

How to cite

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Ivan 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

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  1. [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. [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. [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. [4] I. Chajda, R. Halaš and J. Kühr, Semilattice Structures (Heldermann Verlag (Lemgo, Germany), 2007). 
  5. [5] P. Hájek, On very true, Fuzzy Sets and Systems 124 (2001) 329-333. Zbl0997.03028
  6. [6] L.A. Zadeh, A fuzzy-set-theoretical interpretation of linguistic hedges, J. Cybern. 2 (1972) 4-34. 

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