Sufficient conditions for a T-partial order obtained from triangular norms to be a lattice

Lifeng Li; Jianke Zhang; Chang Zhou

Kybernetika (2019)

  • Volume: 55, Issue: 2, page 295-306
  • ISSN: 0023-5954

Abstract

top
For a t-norm T on a bounded lattice ( L , ≤ ) , a partial order ≤ T was recently defined and studied. In [11], it was pointed out that the binary relation ≤ T is a partial order on L , but ( L , ≤ T ) may not be a lattice in general. In this paper, several sufficient conditions under which ( L , ≤ T ) is a lattice are given, as an answer to an open problem posed by the authors of [11]. Furthermore, some examples of t-norms on L such that ( L , ≤ T ) is a lattice are presented.

How to cite

top

Li, Lifeng, Zhang, Jianke, and Zhou, Chang. "Sufficient conditions for a T-partial order obtained from triangular norms to be a lattice." Kybernetika 55.2 (2019): 295-306. <http://eudml.org/doc/294588>.

@article{Li2019,
abstract = {For a t-norm T on a bounded lattice $(L, \le )$, a partial order $\le _\{T\}$ was recently defined and studied. In [11], it was pointed out that the binary relation $\le _\{T\} $ is a partial order on $L$, but $(L, \le _\{T\} )$ may not be a lattice in general. In this paper, several sufficient conditions under which $(L, \le _\{T\} )$ is a lattice are given, as an answer to an open problem posed by the authors of [11]. Furthermore, some examples of t-norms on $L$ such that $(L, \le _\{T\}) $ is a lattice are presented.},
author = {Li, Lifeng, Zhang, Jianke, Zhou, Chang},
journal = {Kybernetika},
keywords = {bounded lattice; triangular norm; T-partial order},
language = {eng},
number = {2},
pages = {295-306},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Sufficient conditions for a T-partial order obtained from triangular norms to be a lattice},
url = {http://eudml.org/doc/294588},
volume = {55},
year = {2019},
}

TY - JOUR
AU - Li, Lifeng
AU - Zhang, Jianke
AU - Zhou, Chang
TI - Sufficient conditions for a T-partial order obtained from triangular norms to be a lattice
JO - Kybernetika
PY - 2019
PB - Institute of Information Theory and Automation AS CR
VL - 55
IS - 2
SP - 295
EP - 306
AB - For a t-norm T on a bounded lattice $(L, \le )$, a partial order $\le _{T}$ was recently defined and studied. In [11], it was pointed out that the binary relation $\le _{T} $ is a partial order on $L$, but $(L, \le _{T} )$ may not be a lattice in general. In this paper, several sufficient conditions under which $(L, \le _{T} )$ is a lattice are given, as an answer to an open problem posed by the authors of [11]. Furthermore, some examples of t-norms on $L$ such that $(L, \le _{T}) $ is a lattice are presented.
LA - eng
KW - bounded lattice; triangular norm; T-partial order
UR - http://eudml.org/doc/294588
ER -

References

top
  1. Birkhoff, G., 10.1090/coll/025, American Mathematical Society Colloquium Publishers, Providence, 1967. Zbl0537.06001MR0227053DOI10.1090/coll/025
  2. Aşıcı, E., Karaçal, F., 10.1016/j.ins.2014.01.032, Inf. Sci. 267 (2014), 323-333. MR3177320DOI10.1016/j.ins.2014.01.032
  3. Aşıcı, E., 10.1016/j.fss.2016.12.004, Fuzzy Sets Syst. 325 (2017), 35-46. MR3690353DOI10.1016/j.fss.2016.12.004
  4. Casasnovas, J., Mayor, G., 10.1016/j.fss.2007.12.005, Fuzzy Sets Syst. 1599 (2008), 1165-1177. Zbl1176.03023MR2416385DOI10.1016/j.fss.2007.12.005
  5. Çaylı, G. D., Karaçal, F., Mesiar, R., 10.1016/j.ins.2016.05.036, Inf. Sci. 367-368 (2016), 221-231. MR3684677DOI10.1016/j.ins.2016.05.036
  6. Çaylı, G. D., 10.1016/j.fss.2017.07.015, Fuzzy Sets Syst. 332 (2018), 129-143. MR3732255DOI10.1016/j.fss.2017.07.015
  7. Clifford, A. H., 10.2307/2372706, Amer. J. Math. 76 (1954), 631-646. MR0062118DOI10.2307/2372706
  8. Drygaś, P., 10.1007/978-3-540-72950-1_19, In: Soft Computing Foundations and Theoretical Aspect (K. Atanassov, O. Hryniewicz, and J. Kacprzyk,eds.), EXIT, Warszawa 2004, pp. 181-190. DOI10.1007/978-3-540-72950-1_19
  9. Ertuvgrul, Ü., Kesiciovglu, M. N., Karaçal, F., 10.1016/j.ins.2015.10.019, Inform. Sci. 330 (2016), 315-327. DOI10.1016/j.ins.2015.10.019
  10. Hartwig, R., How to partially order regular elements., Math. Japon. 25 (1980), 1-13. MR0571255
  11. Karaçal, F., Kesiciovglu, M. N., A T-partial order obtained from t-norms., Kybernetika 47 (2011), 300-314. MR2828579
  12. Karaçal, F., İnce, M. A., Mesiar, R., 10.1016/j.ins.2015.06.052, Inf. Sci. 325 (2015), 227-236. MR3392300DOI10.1016/j.ins.2015.06.052
  13. Kesiciovglu, M.N., Karaçal, F., Mesiar, R., 10.1016/j.fss.2014.10.006, Fuzzy Sets Syst. 268 (2015), 59-71. MR3320247DOI10.1016/j.fss.2014.10.006
  14. Klement, E. P., Mesiar, R., Pap, E., 10.1007/978-94-015-9540-7, Kluwer Academic Publishers, Dordrecht 2000. Zbl1087.20041MR1790096DOI10.1007/978-94-015-9540-7
  15. Lawson, M., The natural partial order on an abundant semigroup., Proc. Edinburgh Math. Soc. 30 (1987), 2, 169-186. MR0892688
  16. Lu, J., Wang, K. Y., Zhao, B., 10.1016/j.fss.2017.07.013, Fuzzy Sets Syst. 334 (2018), 73-82. MR3742233DOI10.1016/j.fss.2017.07.013
  17. Mitsch, H., 10.1090/s0002-9939-1986-0840614-0, Proc. Amer. Math. Soc. 97 (1986), 384-388. Zbl0596.06015MR0840614DOI10.1090/s0002-9939-1986-0840614-0

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.