owmax {agop} | R Documentation |

## WMax, WMin, OWMax, and OWMin Operators

### Description

Computes the (Ordered) Weighted Maximum/Minimum.

### Usage

owmax(x, w = rep(Inf, length(x))) owmin(x, w = rep(-Inf, length(x))) wmax(x, w = rep(Inf, length(x))) wmin(x, w = rep(-Inf, length(x)))

### Arguments

`x` |
numeric vector to be aggregated |

`w` |
numeric vector of the same length as |

### Details

The OWMax operator is given by

*
OWMax_w(x) = max_i{ min{w_i, x_(i)} }
*

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

.

The OWMin operator is given by

*
OWMin_w(x) = min_i{ max{w_i, x_(i)} }
*

The WMax operator is given by

*
WMax_w(x) = max_i{ min{w_i, x_i} }
*

The WMin operator is given by

*
WMin_w(x) = min_i{ max{w_i, x_i} }
*

`OWMax`

and `WMax`

return the greatest value in `x`

by default, and `OWMin`

and `WMin`

- the smallest value in `x`

.

Classically, it is assumed that if we agregate
vectors with elements in *[a,b]*, then
the largest weight for OWMax should be equal to *b*
and the smallest for OWMin should be equal to *a*.

There is a strong connection between the OWMax/OWMin operators and the Sugeno integrals w.r.t. some monotone measures. Additionally, it may be shown that the OWMax and OWMin classes are equivalent.

Moreover, `index_h`

for integer data
is a particular OWMax operator.

### Value

These functions return a single numeric value.

### References

Dubois D., Prade H., Testemale C., Weighted fuzzy pattern matching,
*Fuzzy Sets and Systems* 28, 1988, pp. 313-331.

Dubois D., Prade H., Semantics of quotient operators in fuzzy
relational databases, *Fuzzy Sets and Systems* 78(1), 1996, pp. 89-93.

Sugeno M., *Theory of fuzzy integrals and its applications*,
PhD thesis, Tokyo Institute of Technology, 1974.

### See Also

Other aggregation_operators: `owa`

,
`wam`

*agop*version 0.2-0 Index]