Computes the (Ordered) Weighted Maximum/Minimum.
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)))
numeric vector to be aggregated
numeric vector of the same length as x; weights
single numeric value
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 greatest
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 return the greatest value in x
by default, and OWMin and WMin - the smallest value in x.
Note that e.g. in the case of OWMax operator
the aggregation w.r.t. w gives the same result as
that of w.r.t. sort(w).
Moreover, classically, it is assumed that if we agregate
vectors with elements in \([a,b]\), then
the largest weight should be equal to \(b\).
There is a strong connection between the OWMax/OWMin operators and the Sugeno integrals. Additionally, it may be shown that the OWMax and OWMin classes are equivalent.
Moreover, index_h for integer data
is a particular OWMax operator.
Dubois D., Prade H., Testemale C., Weighted fuzzy pattern matching, Fuzzy Sets and Systems 28, 1988, pp. 313-331.