Computes the Weighted Arithmetic Mean or the Ordered Weighted Averaging aggregation operator.
owa(x, w = rep(1/length(x), length(x)))wam(x, w = rep(1/length(x), length(x)))
These functions return a single numeric value.
numeric vector to be aggregated
numeric vector of the same length as x, with elements in \([0,1]\),
and such that \(\sum_i w_i=1\); weights
The OWA operator is given by
$$
\mathsf{OWA}_\mathtt{w}(\mathtt{x})=\sum_{i=1}^{n} w_{i}\,x_{(i)}
$$
where \(x_{(i)}\) denotes the \(i\)-th smallest
value in x.
The WAM operator is given by $$ \mathsf{WAM}_\mathtt{w}(\mathtt{x})=\sum_{i=1}^{n} w_{i}\,x_{i} $$
If the elements in w do not sum up to \(1\), then
they are normalized and a warning is generated.
Both functions by default return the ordinary arithmetic mean.
Special cases of OWA include the trimmed mean (see mean)
and Winsorized mean.
There is a strong, well-known connection between the OWA operators and the Choquet integrals.
Choquet G., Theory of capacities, Annales de l'institut Fourier 5, 1954, pp. 131-295.
Gagolewski M., Data Fusion: Theory, Methods, and Applications, Institute of Computer Science, Polish Academy of Sciences, 2015, 290 pp. isbn:978-83-63159-20-7
Yager R.R., On ordered weighted averaging aggregation operators in multicriteria decision making, IEEE Transactions on Systems, Man, and Cybernetics 18(1), 1988, pp. 183-190.
Other aggregation_operators:
owmax()