Geodesic
Möbius fitting aggregation operators
Kybernetika, Tome 38 (2002) no. 3, pp. 259-273 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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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     title = {M\"obius fitting aggregation operators},
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     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, pp. 259-273. http://geodesic.mathdoc.fr/item/KYB_2002_38_3_a3/

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