owa {agop}

WAM and OWA Operators

Description

Computes the Weighted Arithmetic Mean or the Ordered Weighted Averaging aggregation operator.

Usage

owa(x, w = rep(1/length(x), length(x)))

wam(x, w = rep(1/length(x), length(x)))

Arguments

x

numeric vector to be aggregated

w

numeric vector of the same length as x, with elements in [0,1], and such that \sum_i w_i=1; weights

Details

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.

Value

These functions return a single numeric value.

References

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.

See Also

Other aggregation_operators: owmax()