owa {agop} R Documentation

## 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(x)=1; weights

### Details

The OWA operator is given by

OWA_w(x) = sum_i(w_i * x_(i))

where x_(i) denotes the i-th smallest value in `x`.

The WAM operator is given by

WAM_w(x) = sum_i(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.

Other aggregation_operators: `owmax`