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

```
\mathsf{OWMax}_\mathtt{w}(\mathtt{x})=\bigvee_{i=1}^{n} w_{i}\wedge x_{(i)}
```

where `x_{(i)}`

denotes the `i`

-th smallest
value in `x`

.

The OWMin operator is given by

```
\mathsf{OWMin}_\mathtt{w}(\mathtt{x})=\bigwedge_{i=1}^{n} w_{i}\vee x_{(i)}
```

The WMax operator is given by

```
\mathsf{WMax}_\mathtt{w}(\mathtt{x})=\bigvee_{i=1}^{n} w_{i}\wedge x_{i}
```

The WMin operator is given by

```
\mathsf{WMin}_\mathtt{w}(\mathtt{x})=\bigwedge_{i=1}^{n} w_{i}\vee x_{i}
```

`OWMax`

and `WMax`

by default return the greatest value in `x`

and `OWMin`

and `WMin`

- the smallest value in `x`

.

Classically, it is assumed that if we aggregate
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.

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

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

### See Also

Other aggregation_operators:
`owa()`

*agop*version 0.2.4 Index]