owa {agop} | R Documentation |

## WAM and OWA Operators

### Description

Computes the Weghted 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

*
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 of `w`

does not sum up to *1*, then
they are normalized and a warning is generated.

Both functions return the ordinary arithmetic mean by default.
Special cases of OWA include the trimmed mean (cf. `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.

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`

,
`owmin`

, `wmax`

,
`wmin`

*agop*version 0.2-0 Index]