About the equivalence of nullnorms on bounded lattice

M. Nesibe Kesicioğlu

Kybernetika (2017)

  • Volume: 53, Issue: 5, page 877-891
  • ISSN: 0023-5954

Abstract

top
In this paper, an equivalence on the class of nullnorms on a bounded lattice based on the equality of the orders induced by nullnorms is introduced. The set of all incomparable elements w.r.t. the order induced by nullnorms is investigated. Finally, the recently posed open problems have been solved.

How to cite

top

Kesicioğlu, M. Nesibe. "About the equivalence of nullnorms on bounded lattice." Kybernetika 53.5 (2017): 877-891. <http://eudml.org/doc/294490>.

@article{Kesicioğlu2017,
abstract = {In this paper, an equivalence on the class of nullnorms on a bounded lattice based on the equality of the orders induced by nullnorms is introduced. The set of all incomparable elements w.r.t. the order induced by nullnorms is investigated. Finally, the recently posed open problems have been solved.},
author = {Kesicioğlu, M. Nesibe},
journal = {Kybernetika},
keywords = {nullnorm; nounded lattice; partial order; equivalence},
language = {eng},
number = {5},
pages = {877-891},
publisher = {Institute of Information Theory and Automation AS CR},
title = {About the equivalence of nullnorms on bounded lattice},
url = {http://eudml.org/doc/294490},
volume = {53},
year = {2017},
}

TY - JOUR
AU - Kesicioğlu, M. Nesibe
TI - About the equivalence of nullnorms on bounded lattice
JO - Kybernetika
PY - 2017
PB - Institute of Information Theory and Automation AS CR
VL - 53
IS - 5
SP - 877
EP - 891
AB - In this paper, an equivalence on the class of nullnorms on a bounded lattice based on the equality of the orders induced by nullnorms is introduced. The set of all incomparable elements w.r.t. the order induced by nullnorms is investigated. Finally, the recently posed open problems have been solved.
LA - eng
KW - nullnorm; nounded lattice; partial order; equivalence
UR - http://eudml.org/doc/294490
ER -

References

top
  1. Aşıcı, E., 10.1016/j.fss.2016.12.004, Fuzzy Sets and Systems 325 (2017), 35-46. MR3690353DOI10.1016/j.fss.2016.12.004
  2. Baczyński, M., Jayaram, B., Fuzzy Implications., Springer 2008. Zbl1293.03012
  3. Birkhoff, G., 10.1090/coll/025, Providence 1967. Zbl0537.06001MR0227053DOI10.1090/coll/025
  4. Calvo, T., Baets, B. De, Fodor, J., 10.1016/s0165-0114(99)00125-6, Fuzzy Sets and Systems 120 (2001), 385-394. Zbl0977.03026MR1829256DOI10.1016/s0165-0114(99)00125-6
  5. Dubois, D., Prade, H., 10.1016/0020-0255(85)90027-1, Inform. Sci. 36 (1985), 85-121. Zbl0582.03040MR0813766DOI10.1016/0020-0255(85)90027-1
  6. Ertuğrul, Ü., Kesicioğlu, M. N., Karaçal, F., 10.1016/j.ins.2015.10.019, Inform. Sci. 330 (2016), 315-327. DOI10.1016/j.ins.2015.10.019
  7. Grabisch, M., Marichal, J.-L., Mesiar, R., Pap, E., Aggregation Functions., Cambridge University Press 2009. Zbl1206.68299MR2538324
  8. Hliněná, D., Kalina, M., Král, P., Pre-orders and orders generated by conjunctive uninorms., In: 12th International Conference on Fuzzy Set Theory and Its Applications. Communications in Computer and Inform. Sci. 444 (2014), 307-316. MR3616458
  9. Karaçal, F., Ince, M. A., Mesiar, R., 10.1016/j.ins.2015.06.052, Inform. Sci. 325 (2015), 227-236. MR3392300DOI10.1016/j.ins.2015.06.052
  10. Karaçal, F., Mesiar, R., 10.1016/j.fss.2014.05.001, Fuzzy Sets and Systems 261 (2015), 33-43. MR3291484DOI10.1016/j.fss.2014.05.001
  11. Karaçal, F., Kesicioğlu, M. N., A T-partial order obtained from t-norms., Kybernetika 47 (2011), 300-314. Zbl1245.03086MR2828579
  12. Kesicioğlu, M. N., Ertuğrul, Ü., Karaçal, F., 10.1016/j.ins.2017.05.020, Inform. Sci. 411 (2017), 39-51. MR3659313DOI10.1016/j.ins.2017.05.020
  13. Kesicioğlu, M. N., Karaçal, F., Mesiar, R., Order-equivalent triangular norms., Fuzzy Sets and Systems 268 (2015), 59-71. MR3320247
  14. Kesicioğlu, M. N., Mesiar, R., 10.1016/j.ins.2013.12.047, Inform. Sci. 276 (2014), 377-386. MR3206505DOI10.1016/j.ins.2013.12.047
  15. Klement, E. P., Mesiar, R., Pap, E., 10.1007/978-94-015-9540-7, Kluwer Academic Publishers 2000. Zbl1087.20041MR1790096DOI10.1007/978-94-015-9540-7
  16. Ma, Z., Wu, W. M., 10.1016/0020-0255(91)90007-H, Inform. Sci. 55 (1991), 77-97. Zbl0741.03010MR1080449DOI10.1016/0020-0255(91)90007-H
  17. Mas, M., Mayor, G., Torrens, J., 10.1142/s0218488599000039, Int. J. Uncertainty Fuzziness Knowledge-Based Syst. 7 (1999), 31-50. Zbl1005.03047MR1691482DOI10.1142/s0218488599000039
  18. Mas, M., Mayor, G., Torrens, J., 10.1016/s0165-0114(01)00055-0, Fuzzy Sets and Systems 126 (2002), 207-218. MR1884687DOI10.1016/s0165-0114(01)00055-0
  19. Yager, R. R., 10.1016/0165-0114(94)90082-5, Fuzzy Sets and Systems 67 (1994), 129-145. MR1302575DOI10.1016/0165-0114(94)90082-5

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.