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)))
x;
weightsx.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.
owa,
wam