Geodesic
Notes on locally internal uninorm on bounded lattices
Kybernetika, Tome 53 (2017) no. 5, pp. 911-921
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In the study, we introduce the definition of a locally internal uninorm on an arbitrary bounded lattice $L$. We examine some properties of an idempotent and locally internal uninorm on an arbitrary bounded latice $L$, and investigate relationship between these operators. Moreover, some illustrative examples are added to show the connection between idempotent and locally internal uninorm.
In the study, we introduce the definition of a locally internal uninorm on an arbitrary bounded lattice $L$. We examine some properties of an idempotent and locally internal uninorm on an arbitrary bounded latice $L$, and investigate relationship between these operators. Moreover, some illustrative examples are added to show the connection between idempotent and locally internal uninorm.
DOI : 10.14736/kyb-2017-5-0911
Classification : 03B52, 03E72, 06B20
Keywords: bounded lattice; uninorm; idempotent uninorm; locally internal 
@article{10_14736_kyb_2017_5_0911,
     author = {\c{C}ayl{\i}, G\"ul Deniz and Ertu\u{g}rul, \"Umit and K\"oro\u{g}lu, Tuncay and Kara\c{c}al, Funda},
     title = {Notes on locally internal uninorm on bounded lattices},
     journal = {Kybernetika},
     pages = {911--921},
     year = {2017},
     volume = {53},
     number = {5},
     doi = {10.14736/kyb-2017-5-0911},
     mrnumber = {3750111},
     zbl = {06861632},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2017-5-0911/}
}
TY  - JOUR
AU  - Çaylı, Gül Deniz
AU  - Ertuğrul, Ümit
AU  - Köroğlu, Tuncay
AU  - Karaçal, Funda
TI  - Notes on locally internal uninorm on bounded lattices
JO  - Kybernetika
PY  - 2017
SP  - 911
EP  - 921
VL  - 53
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.14736/kyb-2017-5-0911/
DO  - 10.14736/kyb-2017-5-0911
LA  - en
ID  - 10_14736_kyb_2017_5_0911
ER  - 
%0 Journal Article
%A Çaylı, Gül Deniz
%A Ertuğrul, Ümit
%A Köroğlu, Tuncay
%A Karaçal, Funda
%T Notes on locally internal uninorm on bounded lattices
%J Kybernetika
%D 2017
%P 911-921
%V 53
%N 5
%U http://geodesic.mathdoc.fr/articles/10.14736/kyb-2017-5-0911/
%R 10.14736/kyb-2017-5-0911
%G en
%F 10_14736_kyb_2017_5_0911
Çaylı, Gül Deniz; Ertuğrul, Ümit; Köroğlu, Tuncay; Karaçal, Funda. Notes on locally internal uninorm on bounded lattices. Kybernetika, Tome 53 (2017) no. 5, pp. 911-921. doi: 10.14736/kyb-2017-5-0911

[1] Aşıcı, E., Karaçal, F.: Incomparability with respect to the triangular order. Kybernetika 52 (2016), 15-27. | DOI | MR

[2] Birkhoff, G.: Lattice Theory. American Mathematical Society Colloquium Publ., Providence 1967. | DOI | MR | Zbl

[3] Baets, B. De: Idempotent uninorms. European J. Oper. Res. 118 (1999), 631-642. | DOI | Zbl

[4] Baets, B. De, Fodor, J.: A single-point characterization of representable uninorms. Fuzzy Sets Syst. 202 (2012), 89-99. | DOI | MR

[5] Çaylı, G. D., Karaçal, F., Mesiar, R.: On a new class of uninorms on bounded lattices. Inform. Sci. 367-368 (2016), 221-231. | DOI | MR

[6] Çaylı, G. D., Drygaś, P.: Some properties of idempotent uninorms on bounded lattices. Inform. Sci. 422 (2018), 352-363. | DOI | MR

[7] Drewniak, J., Drygaś, P.: On a class of uninorms. Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 10 (2002), 5-10. | DOI | MR

[8] Drygaś, P.: On properties of uninorms with underlying t-norm and t-conorm given as ordinal sums. Fuzzy Sets Syst. 161 (2010), 149-157. | DOI | MR | Zbl

[9] Drygaś, P., Ruiz-Aguilera, D., Torrens, J.: A characterization of uninorms locally internal in $A(e)$ with continuous underlying operators. Fuzzy Sets Syst. 287 (2016), 137-153. | DOI | MR

[10] Ertuğrul, Ü., Kesicioğlu, M. N., Karaçal, F.: Ordering based on uninorms. Inform. Sci. 330 (2016), 315-327. | DOI

[11] Fodor, J., Yager, R. R., Rybalov, A.: Structure of uninorms. Int. J. Uncertain Fuzziness Knowl.-Based Syst. 5 (1997), 411-427. | DOI | MR | Zbl

[12] Kesicioğlu, M. N., Mesiar, R.: Ordering based on implications. Fuzzy Sets Syst. 276 (2014), 377-386. | DOI | MR

[13] Kesicioğlu, M. N., Ertuğrul, Ü., Karaçal, F.: An equivalence relation based on the U-partial order. Inform. Sci. 411 (2017), 39-51. | DOI | MR

[14] Karaçal, F., Mesiar, R.: Uninorms on bounded lattices. Fuzzy Sets Syst. 261 (2015), 33-43. | DOI | MR

[15] Karaçal, F., Ertuğrul, Ü., Mesiar, R.: Characterization of uninorms on bounded lattices. Fuzzy Sets Syst. 308 (2017), 54-71. | DOI | MR

[16] Klement, E. P., Mesiar, R., Pap, E.: Triangular Norms. Dordrecht, Kluwer Acad. Publ., 2000. | DOI | MR | Zbl

[17] Martin, J., Mayor, G., Torrens, J.: On locally internal monotonic operations. Fuzzy Sets Syst. 137 (2003), 27-42. | DOI | MR | Zbl

[18] Mesiarová-Zemánková, A.: Multi-polar t-conorms and uninorms. Inform. Sci. 301 (2015), 227-240. | DOI | MR

[19] Yager, R. R.: Uninorms in fuzzy system modeling. Fuzzy Sets Syst. 122 (2001), 167-175. | DOI | MR

[20] Yager, R. R.: Defending against strategic manipulation in uninorm-based multi-agent decision making. European J. Oper. Res. 141 (2002), 217-232. | DOI | MR | Zbl

[21] Yager, R. R., Rybalov, A.: Uninorms aggregation operators. Fuzzy Sets Syst. 80 (1996), 111-120. | DOI | MR

Cité par Sources :