Previous |  Up |  Next


uninorm; triangular norm; triangular conorm; binary operation; increasing operation; idempotent operation; associative operation
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.
[1] Czogała E., Drewniak J.: Associative monotonic operations in fuzzy set theory. Fuzzy Sets and Systems 12 (1984), 249–269 DOI 10.1016/0165-0114(84)90072-1 | MR 0740097 | Zbl 0555.94027
[2] Baets B. De: Idempotent uninorms. European J. Oper. Res. 118 (1999), 631–642 DOI 10.1016/S0377-2217(98)00325-7 | Zbl 0933.03071
[3] Drewniak J., Drygaś P.: On a class of uninorms. Internat. J. Uncertainty, Fuzziness and Knowledge-based Systems 10 (2002), Supplement, 5–10 DOI 10.1142/S021848850200179X | MR 1962665 | Zbl 1053.03510
[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 10.1142/S0218488597000312 | MR 1471619 | Zbl 1232.03015
[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 1884686
[7] Klement E. P., Mesiar, R., Pap E.: Triangular Norms. Kluwer Academic Publishers, Dordrecht 2000 MR 1790096 | Zbl 1087.20041
[8] Li Y.-M., Shi Z.-K.: Remarks on uninorm aggregation operators. Fuzzy Sets and Systems 114 (2000), 377–380 DOI 10.1016/S0165-0114(98)00247-4 | MR 1775275 | Zbl 0962.03052
[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 1992696
[11] Yager R., Rybalov A.: Uninorm aggregation operators. Fuzzy Sets and Systems 80 (1996), 111–120 DOI 10.1016/0165-0114(95)00133-6 | MR 1389951 | Zbl 0871.04007
Partner of
EuDML logo