https://github.com/cran/kappalab
Tip revision: 085a64b3faed6893ba219fbdb8aa3e2e0d3f56f1 authored by Ivan Kojadinovic on 18 July 2015, 00:00:00 UTC
version 0.4-7
version 0.4-7
Tip revision: 085a64b
Sipos.integral-methods.Rd
\name{Sipos.integral-methods}
\docType{methods}
\alias{Sipos.integral}
\alias{Sipos.integral-methods}
\alias{Sipos.integral,Mobius.game,numeric-method}
\alias{Sipos.integral,card.game,numeric-method}
\alias{Sipos.integral,game,numeric-method}
\title{Sipos integral}
\description{Computes the Sipos integral (also called \emph{symmetric Choquet
integral}) of a real-valued function with respect to a game. The game can be
given either under the form of an object of class \code{game},
\code{card.game} or \code{Mobius.game}.}
\section{Methods}{
\describe{
\item{object = "game", f = "numeric" }{The Sipos or symmetric Choquet integral of \code{f}
is computed from a game.}
\item{object = "Mobius.game", f = "numeric" }{The Sipos or symmetric Choquet integral of
\code{f} is computed from the \enc{M—bius}{Mobius} transform of a game.}
\item{object = "card.game", f = "numeric" }{The Sipos or symmetric Choquet integral of
\code{f} is computed from a cardinal game.}
}}
\references{
M. Grabisch and Ch. Labreuche (2002), The symmetric and asymmetric Choquet
integrals on finite spaces for decision making, Statistical Papers 43, pages
37-52.
}
\seealso{
\code{\link{game-class}},
\cr \code{\link{Mobius.game-class}},
\cr \code{\link{card.game-class}}.
}
\examples{
## a normalized capacity
mu <- capacity(c(0:13/13,1,1))
## and its Mobius transform
a <- Mobius(mu)
## a discrete function f
f <- c(0.1,-0.9,-0.3,0.8)
## the Sugeno integral of f w.r.t mu
Sipos.integral(mu,f)
Sipos.integral(a,f)
## a similar example with a cardinal capacity
mu <- uniform.capacity(4)
Sipos.integral(mu,f)
}
\keyword{methods}
%\keyword{ ~~ other possible keyword(s)}