An extension method for t-norms on subintervals to t-norms on bounded lattices

Funda Karaçal; Ümit Ertuğrul; M. Nesibe Kesicioğlu

Kybernetika (2019)

  • Volume: 55, Issue: 6, page 976-993
  • ISSN: 0023-5954

Abstract

top
In this paper, a construction method on a bounded lattice obtained from a given t-norm on a subinterval of the bounded lattice is presented. The supremum distributivity of the constructed t-norm by the mentioned method is investigated under some special conditions. It is shown by an example that the extended t-norm on L from the t-norm on a subinterval of L need not be a supremum-distributive t-norm. Moreover, some relationships between the mentioned construction method and the other construction methods in the literature are presented.

How to cite

top

Karaçal, Funda, Ertuğrul, Ümit, and Kesicioğlu, M. Nesibe. "An extension method for t-norms on subintervals to t-norms on bounded lattices." Kybernetika 55.6 (2019): 976-993. <http://eudml.org/doc/297135>.

@article{Karaçal2019,
abstract = {In this paper, a construction method on a bounded lattice obtained from a given t-norm on a subinterval of the bounded lattice is presented. The supremum distributivity of the constructed t-norm by the mentioned method is investigated under some special conditions. It is shown by an example that the extended t-norm on $L$ from the t-norm on a subinterval of $L$ need not be a supremum-distributive t-norm. Moreover, some relationships between the mentioned construction method and the other construction methods in the literature are presented.},
author = {Karaçal, Funda, Ertuğrul, Ümit, Kesicioğlu, M. Nesibe},
journal = {Kybernetika},
keywords = {T-norm; bounded lattice; construction method; subinterval},
language = {eng},
number = {6},
pages = {976-993},
publisher = {Institute of Information Theory and Automation AS CR},
title = {An extension method for t-norms on subintervals to t-norms on bounded lattices},
url = {http://eudml.org/doc/297135},
volume = {55},
year = {2019},
}

TY - JOUR
AU - Karaçal, Funda
AU - Ertuğrul, Ümit
AU - Kesicioğlu, M. Nesibe
TI - An extension method for t-norms on subintervals to t-norms on bounded lattices
JO - Kybernetika
PY - 2019
PB - Institute of Information Theory and Automation AS CR
VL - 55
IS - 6
SP - 976
EP - 993
AB - In this paper, a construction method on a bounded lattice obtained from a given t-norm on a subinterval of the bounded lattice is presented. The supremum distributivity of the constructed t-norm by the mentioned method is investigated under some special conditions. It is shown by an example that the extended t-norm on $L$ from the t-norm on a subinterval of $L$ need not be a supremum-distributive t-norm. Moreover, some relationships between the mentioned construction method and the other construction methods in the literature are presented.
LA - eng
KW - T-norm; bounded lattice; construction method; subinterval
UR - http://eudml.org/doc/297135
ER -

References

top
  1. G., Birkhoff,, 10.1090/coll/025, Providence 1967. MR0227053DOI10.1090/coll/025
  2. D., Çaylı, G., 10.1016/j.fss.2017.07.015, Fuzzy Sets and Systems 332 (2018), 129-143. MR3732255DOI10.1016/j.fss.2017.07.015
  3. P., Drygaś,, B., Pekala,, Properties of decomposable operations on same etension of the fuzzy set theory., In: Advences in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets and Related Topics (K. T. Atanassov, O. Hryniewicz, J. Kacprzyk, M. Krawczak, Z. Nahorski, E. Szmidt, S. Zadrozny, eds.), Vol. I, Foundations, EXIT, Warszawa 2008, pp. 115-118. MR1478260
  4. Ü., Ertuğrul,, F., Karaçal,, R., Mesiar,, 10.1002/int.21713, Int. J. Intell. Systems 30 (2015), 807-817. DOI10.1002/int.21713
  5. M., Grabisch,, L., Marichal, J., R., Mesiar,, E., Pap,, 10.1017/cbo9781139644150, Cambridge University Press, 2009. Zbl1206.68299MR2538324DOI10.1017/cbo9781139644150
  6. F., Karaçal,, 10.1016/j.ins.2005.12.010, Inform. Sci. 176 (2006), 3011-3025. Zbl1104.03016MR2247614DOI10.1016/j.ins.2005.12.010
  7. F., Karaçal,, D., Khadjiev,, 10.1016/j.fss.2004.06.013, Fuzzy Sets Systems 151 (2005), 341-352. MR2124884DOI10.1016/j.fss.2004.06.013
  8. F., Karaçal,, N., Kesicioğlu, M., A T-partial order obtained from t-norms., Kybernetika 47 (2011), 300-314. Zbl1245.03086MR2828579
  9. P, Klement, E.., R., Mesiar,, E., Pap,, Triangular Norms., Kluwer Academic Publishers, Dordrecht 2000. Zbl1087.20041MR1790096
  10. J., Martin,, G., Mayor,, J., Torrens,, 10.1016/s0165-0114(02)00430-x, Fuzzy Sets Syst. 137 (2003), 27-42. Zbl1022.03038MR1992696DOI10.1016/s0165-0114(02)00430-x
  11. K.Menger, 10.1073/pnas.28.12.535, Proc. Natl. Acad. Sci. USA 8 (1942), 535-537. MR0007576DOI10.1073/pnas.28.12.535
  12. S., Saminger,, 10.1016/j.fss.2005.12.021, Fuzzy Sets Systems 157 (2006), 10, 1403-1416. Zbl1099.06004MR2226983DOI10.1016/j.fss.2005.12.021
  13. B., Schweizer,, A., Sklar,, Espaces metriques aléatoires., C. R. Acad. Sci. Paris Ser. A 247 (1958), 2092-2094. MR0099068
  14. B., Schweizer,, A., Sklar,, 10.2140/pjm.1960.10.313, Pacific J. Math. 10 (1960), 313-334. Zbl0136.39301MR0115153DOI10.2140/pjm.1960.10.313
  15. K., Tsadiras, A., G., Margaritis, R., 10.1016/s0165-0114(96)00185-6, Fuzzy Sets Syst. 93 (1998), 263-274. MR1605312DOI10.1016/s0165-0114(96)00185-6

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.