Geodesic
Discussion of the structure of uninorms
Kybernetika, Tome 41 (2005) no. 2, pp. 213-226 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

The paper deals with binary operations in the unit interval. We investigate connections between families of triangular norms, triangular conorms, uninorms and some decreasing functions. It is well known, that every uninorm is build by using some triangular norm and some triangular conorm. If we assume, that uninorm fulfils additional assumptions, then this triangular norm and this triangular conorm have to be ordinal sums. The intervals in ordinal sum are depending on the set of values of a decreasing function.
The paper deals with binary operations in the unit interval. We investigate connections between families of triangular norms, triangular conorms, uninorms and some decreasing functions. It is well known, that every uninorm is build by using some triangular norm and some triangular conorm. If we assume, that uninorm fulfils additional assumptions, then this triangular norm and this triangular conorm have to be ordinal sums. The intervals in ordinal sum are depending on the set of values of a decreasing function.
Classification : 03B52, 03E72, 06F05
Keywords: uninorm; triangular norm; triangular conorm; binary operation; increasing operation; idempotent operation; associative operation 
@article{KYB_2005_41_2_a7,
     author = {Dryga\'s, Pawe{\l}},
     title = {Discussion of the structure of uninorms},
     journal = {Kybernetika},
     pages = {213--226},
     year = {2005},
     volume = {41},
     number = {2},
     mrnumber = {2138769},
     zbl = {1249.03093},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2005_41_2_a7/}
}
TY  - JOUR
AU  - Drygaś, Paweł
TI  - Discussion of the structure of uninorms
JO  - Kybernetika
PY  - 2005
SP  - 213
EP  - 226
VL  - 41
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/KYB_2005_41_2_a7/
LA  - en
ID  - KYB_2005_41_2_a7
ER  - 
%0 Journal Article
%A Drygaś, Paweł
%T Discussion of the structure of uninorms
%J Kybernetika
%D 2005
%P 213-226
%V 41
%N 2
%U http://geodesic.mathdoc.fr/item/KYB_2005_41_2_a7/
%G en
%F KYB_2005_41_2_a7
Drygaś, Paweł. Discussion of the structure of uninorms. Kybernetika, Tome 41 (2005) no. 2, pp. 213-226. http://geodesic.mathdoc.fr/item/KYB_2005_41_2_a7/

[1] Czogała E., Drewniak J.: Associative monotonic operations in fuzzy set theory. Fuzzy Sets and Systems 12 (1984), 249–269 | DOI | MR | Zbl

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

[3] Drewniak J., Drygaś P.: On a class of uninorms. Internat. J. Uncertainty, Fuzziness and Knowledge-based Systems 10 (2002), Supplement, 5–10 | DOI | MR | Zbl

[4] Fodor J., Baets, B. De, Calvo T.: Characterization of uninorms with given underlying t-norms and t-conorms, submitte.

[5] Fodor J., Yager, R., Rybalov A.: Structure of uninorms. Internat. J. Uncertainty, Fuzziness and Knowledge-based Systems 5 (1997), 411–427 | DOI | MR | Zbl

[6] Jenei S.: A note on the ordinal sum theorem and its consequence for the construction of triangular norm. Fuzzy Sets and Systems 126 (2002), 199–205 | MR

[7] Klement E. P., Mesiar, R., Pap E.: Triangular Norms. Kluwer Academic Publishers, Dordrecht 2000 | MR | Zbl

[8] Li Y.-M., Shi Z.-K.: Remarks on uninorm aggregation operators. Fuzzy Sets and Systems 114 (2000), 377–380 | DOI | MR | Zbl

[9] Martin J.: On a theorem of Czogała and Drewniak (1984). In: Proc. EUROFUSE PM’01, Granada 2001, pp. 49–54

[10] Martin J., Mayor G., and, Torrens J.: On locally internal monotonic operations. Fuzzy Sets and Systems 137 (2003), 27–42 | MR

[11] Yager R., Rybalov A.: Uninorm aggregation operators. Fuzzy Sets and Systems 80 (1996), 111–120 | DOI | MR | Zbl