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 |

### 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()`

*agop*version 0.2.4 Index]