Discussion of the structure of uninorms

Paweł Drygaś

Kybernetika (2005)

  • Volume: 41, Issue: 2, page [213]-226
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Drygaś, Paweł. "Discussion of the structure of uninorms." Kybernetika 41.2 (2005): [213]-226. <http://eudml.org/doc/33750>.

@article{Drygaś2005,
abstract = {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.},
author = {Drygaś, Paweł},
journal = {Kybernetika},
keywords = {uninorm; triangular norm; triangular conorm; binary operation; increasing operation; idempotent operation; associative operation; uninorm; triangular norm; triangular conorm; increasing operation; idempotent operation},
language = {eng},
number = {2},
pages = {[213]-226},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Discussion of the structure of uninorms},
url = {http://eudml.org/doc/33750},
volume = {41},
year = {2005},
}

TY - JOUR
AU - Drygaś, Paweł
TI - Discussion of the structure of uninorms
JO - Kybernetika
PY - 2005
PB - Institute of Information Theory and Automation AS CR
VL - 41
IS - 2
SP - [213]
EP - 226
AB - 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.
LA - eng
KW - uninorm; triangular norm; triangular conorm; binary operation; increasing operation; idempotent operation; associative operation; uninorm; triangular norm; triangular conorm; increasing operation; idempotent operation
UR - http://eudml.org/doc/33750
ER -

References

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  3. Drewniak J., Drygaś P., 10.1142/S021848850200179X, Internat. J. Uncertainty, Fuzziness and Knowledge-based Systems 10 (2002), Supplement, 5–10 Zbl1053.03510MR1962665DOI10.1142/S021848850200179X
  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., 10.1142/S0218488597000312, Internat. J. Uncertainty, Fuzziness and Knowledge-based Systems 5 (1997), 411–427 (1997) Zbl1232.03015MR1471619DOI10.1142/S0218488597000312
  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 MR1884686
  7. Klement E. P., Mesiar, R., Pap E., Triangular Norms, Kluwer Academic Publishers, Dordrecht 2000 Zbl1087.20041MR1790096
  8. Li Y.-M., Shi Z.-K., 10.1016/S0165-0114(98)00247-4, Fuzzy Sets and Systems 114 (2000), 377–380 Zbl0962.03052MR1775275DOI10.1016/S0165-0114(98)00247-4
  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 MR1992696
  11. Yager R., Rybalov A., 10.1016/0165-0114(95)00133-6, Fuzzy Sets and Systems 80 (1996), 111–120 (1996) Zbl0871.04007MR1389951DOI10.1016/0165-0114(95)00133-6

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