Geodesic
Möbius fitting aggregation operators
Kybernetika, Tome 38 (2002) no. 3, p. [259]

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Standard Möbius transform evaluation formula for the Choquet integral is associated with the $\mathbf{min}$-aggregation. However, several other aggregation operators replacing $\mathbf{min}$ operator can be applied, which leads to a new construction method for aggregation operators. All binary operators applicable in this approach are characterized by the 1-Lipschitz property. Among ternary aggregation operators all 3-copulas are shown to be fitting and moreover, all fitting weighted means are characterized. This new method allows to construct aggregation operators from simpler ones.
Classification : 03E72, 28A25, 28E10
Keywords: aggregation operator; Choquet integral 
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     author = {Koles\'arov\'a, Anna},
     title = {M\"obius fitting aggregation operators},
     journal = {Kybernetika},
     pages = {[259]},
     publisher = {mathdoc},
     volume = {38},
     number = {3},
     year = {2002},
     mrnumber = {1944308},
     zbl = {1265.28042},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2002__38_3_a3/}
}
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Kolesárová, Anna. Möbius fitting aggregation operators. Kybernetika, Tome 38 (2002) no. 3, p. [259]. http://geodesic.mathdoc.fr/item/KYB_2002__38_3_a3/