https://github.com/cran/kappalab
Tip revision: 04797bea4a817fcf6daff673777d0c2fc5ae2c45 authored by Ivan Kojadinovic on 07 November 2023, 20:20:02 UTC
version 0.4-12
version 0.4-12
Tip revision: 04797be
orness-methods.Rd
\name{orness-methods}
\docType{methods}
\alias{orness}
\alias{orness-methods}
\alias{orness,Mobius.capacity-method}
\alias{orness,capacity-method}
\alias{orness,card.capacity-method}
\title{Orness degree}
\description{Computes the orness degree of a Choquet integral from the
underlying \bold{normalized} capacity. The capacity can be given either under the form
of an object of class \code{capacity}, \code{card.capacity} or
\code{Mobius.capacity}.}
\section{Methods}{
\describe{
\item{object = "Mobius.capacity" }{The orness degree is computed from the \enc{Möbius}{Mobius} transform of a capacity.}
\item{object = "capacity" }{The orness degree is computed directly from a capacity.}
\item{object = "card.capacity" }{The orness degree is computed from a cardinal capacity.}
}}
\references{
J.-L. Marichal (2000), \emph{Behavioral analysis of aggregation in
multicriteria decision aid}, in Preferences and Decisions under
Incomplete Knowledge, J. Fodor and B. De Baets and P. Perny Eds,
Physica-Verlag, pages 153-178, 2000.
}
\seealso{
\code{\link{capacity-class}},
\cr \code{\link{Mobius.capacity-class}},
\cr \code{\link{card.capacity-class}},
\cr \code{\link{Mobius-methods}}.
}
\examples{
## the upper capacity
mu <- capacity(c(0,rep(1,15)))
## the Choquet integral w.r.t mu behaves like the maximum operator
f <- c(0.1,0.1,0,0.9)
Choquet.integral(mu,f)
## its orness is 1
orness(mu)
## the same example with a Mobius.capacity object
a <- Mobius(mu)
Choquet.integral(a,f)
orness(a)
## the same example with a card.capacity object
mu <- upper.capacity(4)
Choquet.integral(mu,f)
orness(mu)
}
\keyword{methods}
%\keyword{ ~~ other possible keyword(s)}