×

Fitting generated aggregation operators to empirical data. (English) Zbl 1073.28012

The authors discuss the problem of fitting general aggregation operators with unfixed number of arguments to empirical data. Especially they treat triangular norms, uninorms, nullnorms, Choquet integral based operators w.r.t. a general fuzzy measure, OWA-operators and \(k\)-additive symmetric fuzzy measures. Given \(K\) observations of arguments and associated aggregated values the generators of the mentioned operators are fitted by suitable spline approximations. The described approximation methods have been added to the software package “Aggregation operators approximation tool” available from http://www.it.deakin.edu.au/\(\sim\)gleb.

MSC:

28E10 Fuzzy measure theory
65D07 Numerical computation using splines
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1016/0020-0255(85)90027-1 · Zbl 0582.03040 · doi:10.1016/0020-0255(85)90027-1
[2] Klir G., Fuzzy Sets, Uncertainty, and Information (1992)
[3] DOI: 10.1007/978-94-015-8702-0 · doi:10.1007/978-94-015-8702-0
[4] DOI: 10.1007/978-3-7908-1787-4_1 · doi:10.1007/978-3-7908-1787-4_1
[5] DOI: 10.1016/0165-0114(80)90062-7 · Zbl 0435.90009 · doi:10.1016/0165-0114(80)90062-7
[6] DOI: 10.1016/S0165-0114(96)00254-0 · doi:10.1016/S0165-0114(96)00254-0
[7] DOI: 10.1016/0165-0114(84)90097-6 · Zbl 0551.03035 · doi:10.1016/0165-0114(84)90097-6
[8] DOI: 10.1002/int.10120 · Zbl 1074.68607 · doi:10.1002/int.10120
[9] DOI: 10.1142/S0218488502001715 · Zbl 1074.68620 · doi:10.1142/S0218488502001715
[10] DOI: 10.1109/91.971696 · doi:10.1109/91.971696
[11] DOI: 10.1137/1.9781611971217 · doi:10.1137/1.9781611971217
[12] Schweizer B., Probabilistic Metric Spaces (1983) · Zbl 0546.60010
[13] Schweizer B., Publ Math. Debrecen 8 pp 169–
[14] DOI: 10.1007/978-94-015-9540-7 · doi:10.1007/978-94-015-9540-7
[15] DOI: 10.1016/S0165-0114(97)00063-8 · Zbl 0938.03084 · doi:10.1016/S0165-0114(97)00063-8
[16] DOI: 10.1016/S0165-0114(97)00021-3 · Zbl 0938.03083 · doi:10.1016/S0165-0114(97)00021-3
[17] DOI: 10.1007/978-1-4612-6333-3 · doi:10.1007/978-1-4612-6333-3
[18] Dierckx P., Curve and Surface Fitting with Splines (1995) · Zbl 0932.41010
[19] Beliakov G., Approxima tion Theory and Applications 16 pp 80–
[20] DOI: 10.1145/356004.356010 · Zbl 0486.65040 · doi:10.1145/356004.356010
[21] DOI: 10.1007/BF01584232 · Zbl 0461.90056 · doi:10.1007/BF01584232
[22] DOI: 10.1007/3-540-48236-9 · doi:10.1007/3-540-48236-9
[23] DOI: 10.1016/0165-0114(95)00133-6 · Zbl 0871.04007 · doi:10.1016/0165-0114(95)00133-6
[24] DOI: 10.1142/S0218488597000312 · Zbl 1232.03015 · doi:10.1142/S0218488597000312
[25] DOI: 10.1142/S0218488596000081 · Zbl 1232.03041 · doi:10.1142/S0218488596000081
[26] DOI: 10.1016/0377-2217(82)90227-2 · Zbl 0488.90003 · doi:10.1016/0377-2217(82)90227-2
[27] DOI: 10.1016/S0165-0114(99)00125-6 · Zbl 0977.03026 · doi:10.1016/S0165-0114(99)00125-6
[28] DOI: 10.1016/B978-1-4832-5682-5.50004-1 · doi:10.1016/B978-1-4832-5682-5.50004-1
[29] P. Benvenuti and R. Mesiar, Fuzzy Measures and Integrals. Theory and Applications, eds. M. Grabisch, T. Murofushi and M. Sugeno (Physica-Verlag, Heidelberg, 2000) pp. 205–232.
[30] DOI: 10.1016/S0165-0114(97)00168-1 · Zbl 0927.28014 · doi:10.1016/S0165-0114(97)00168-1
[31] M. Grabisch, Fuzzy Measures and Integrals. Theory and Applications, eds. M. Grabisch, T. Murofushi and M. Sugeno (Physica-Verlag, Heidelberg, 2000) pp. 70–93.
[32] DOI: 10.1007/978-3-7908-1796-6_17 · doi:10.1007/978-3-7908-1796-6_17
[33] DOI: 10.1007/978-94-017-2434-0 · doi:10.1007/978-94-017-2434-0
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.