ON CONGRUENCES AND HOMOMORPHISMS ON SOME NON-DETERMINISTIC ALGEBRAS

I. P. Cabrera, P. Cordero, G. Gutiérrez, J. Martínez, M. Ojeda-Aciego

Abstract

Starting with the underlying motivation of developing a general theory of L-fuzzy sets where L is a multilattice (a particular case of non-deterministic algebra), we study the relationship between the crisp notions of congruence, homomorphism and substructure on some non-deterministic algebras which have been used in the literature, i.e. hypergroups, and join spaces. Moreover, we provide suitable extensions of these notions to the fuzzy case.

References

  1. R. Be?lohlávek. Determinism and fuzzy automata. Information Sciences, 143:205-209, 2002.
  2. M. Benado. Les ensembles partiellement ordonnés et le théorème de raffinement de Schreier. I. C? ehoslovack. Mat. Z?., 4(79):105-129, 1954.
  3. I. Cabrera, P. Cordero, G. Gutiérrez, J. Martínez, and M. Ojeda-Aciego. Fuzzy congruence relations on ndgroupoids. Intl J on Computer Mathematics, 2009. To appear.
  4. M. C iric, J. Ignjatovic, and S. Bogdanovic. Uniform fuzzy relations and fuzzy functions. Fuzzy Sets and Systems, 160(8):1054-1081, 2009.
  5. P. Cordero, G. Gutiérrez, J. Martínez, M. Ojeda-Aciego, and I. de las Pen˜as. Congruence relations on multilattices. In Intl FLINS Conference on Computational Intelligence in Decision and Control, FLINS'08, pages 139-144, 2008.
  6. P. Corsini. A new connection between hypergroups and fuzzy sets. Southeast Asian Bull. Math., 27(2):221- 229, 2003.
  7. P. Corsini and V. Leoreanu. Applications of hyperstructure theory. Kluwer, 2003.
  8. B. Davvaz. Some results on congruences on semihypergroups. Bulletin of the Malaysian Mathematical Sciences Society. Second Series, 23(1):53-58, 2000.
  9. M. Demirci. Constructions of fuzzy functions based on fuzzy equalities. Soft Computing, 7(3):199-207, 2003.
  10. G. Gentile. Multiendomorphisms of hypergroupoids. International Mathematical Forum, 1(9-12):563-576, 2006.
  11. J. Goguen. L-fuzzy sets. J. Math. Anal. Appl., 18:145-174, 1967.
  12. T. Janhunen, E. Oikarinen, H. Tompits, and S. Woltran. Modularity aspects of disjunctive stable models. In C. Baral, G. Brewka, and J. S. Schlipf, editors, LPNMR, volume 4483 of Lecture Notes in Computer Science, pages 175-187. Springer, 2007.
  13. F. Klawonn. Fuzzy points, fuzzy relations and fuzzy function. In V. Novák and I. Perfilieva, editors, Discovering World with Fuzzy Logic, pages 431-453. PhysicaVerlag, 2000.
  14. J. Martínez, G. Gutiérrez, I. P. de Guzmán, and P. Cordero. Generalizations of lattices via non-deterministic operators. Discrete Math., 295(1-3):107-141, 2005.
  15. J. Medina, M. Ojeda-Aciego, and J. Ruiz-Calvin˜o. Fuzzy logic programming via multilattices. Fuzzy Sets and Systems, 158(6):674-688, 2007.
  16. E. Oikarinen and T. Janhunen. A translation-based approach to the verification of modular equivalence. Journal of Logic and Computation, 2008. Advance Access published.
  17. T. Petkovic. Congruences and homomorphisms of fuzzy automata. Fuzzy Sets and Systems, 157:444-458, 2006.
Download


Paper Citation


in Harvard Style

Cabrera I., Cordero P., Gutiérrez G., Martínez J. and Ojeda-Aciego M. (2009). ON CONGRUENCES AND HOMOMORPHISMS ON SOME NON-DETERMINISTIC ALGEBRAS . In Proceedings of the International Joint Conference on Computational Intelligence - Volume 1: ICFC, (IJCCI 2009) ISBN 978-989-674-014-6, pages 59-67. DOI: 10.5220/0002313300590067


in Bibtex Style

@conference{icfc09,
author={I. P. Cabrera and P. Cordero and G. Gutiérrez and J. Martínez and M. Ojeda-Aciego},
title={ON CONGRUENCES AND HOMOMORPHISMS ON SOME NON-DETERMINISTIC ALGEBRAS},
booktitle={Proceedings of the International Joint Conference on Computational Intelligence - Volume 1: ICFC, (IJCCI 2009)},
year={2009},
pages={59-67},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0002313300590067},
isbn={978-989-674-014-6},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Joint Conference on Computational Intelligence - Volume 1: ICFC, (IJCCI 2009)
TI - ON CONGRUENCES AND HOMOMORPHISMS ON SOME NON-DETERMINISTIC ALGEBRAS
SN - 978-989-674-014-6
AU - Cabrera I.
AU - Cordero P.
AU - Gutiérrez G.
AU - Martínez J.
AU - Ojeda-Aciego M.
PY - 2009
SP - 59
EP - 67
DO - 10.5220/0002313300590067