# 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

## Access Full Article

top## Abstract

top## How to cite

topLi, 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- Birkhoff, G., 10.1090/coll/025, American Mathematical Society Colloquium Publishers, Providence, 1967. Zbl0537.06001MR0227053DOI10.1090/coll/025
- Aşıcı, E., Karaçal, F., 10.1016/j.ins.2014.01.032, Inf. Sci. 267 (2014), 323-333. MR3177320DOI10.1016/j.ins.2014.01.032
- Aşıcı, E., 10.1016/j.fss.2016.12.004, Fuzzy Sets Syst. 325 (2017), 35-46. MR3690353DOI10.1016/j.fss.2016.12.004
- 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
- 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
- Çaylı, G. D., 10.1016/j.fss.2017.07.015, Fuzzy Sets Syst. 332 (2018), 129-143. MR3732255DOI10.1016/j.fss.2017.07.015
- Clifford, A. H., 10.2307/2372706, Amer. J. Math. 76 (1954), 631-646. MR0062118DOI10.2307/2372706
- 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
- 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
- Hartwig, R., How to partially order regular elements., Math. Japon. 25 (1980), 1-13. MR0571255
- Karaçal, F., Kesiciovglu, M. N., A T-partial order obtained from t-norms., Kybernetika 47 (2011), 300-314. MR2828579
- 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
- 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
- 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
- Lawson, M., The natural partial order on an abundant semigroup., Proc. Edinburgh Math. Soc. 30 (1987), 2, 169-186. MR0892688
- 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
- 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 ?

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