\name{entropy-methods}
\docType{methods}
\alias{entropy}
\alias{entropy-methods}
\alias{entropy,Mobius.capacity-method}
\alias{entropy,capacity-method}
\alias{entropy,card.capacity-method}
\title{Normalized entropy of a capacity}
\description{Computes the normalized entropy of a 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 normalized entropy is computed
from the
\enc{M—bius}{Mobius} transform of a capacity.}
\item{object = "capacity" }{The normalized entropy is computed directly from a capacity.}
\item{object = "card.capacity" }{The normalized entropy is computed from a cardinal capacity.}
}}
\references{
J-L. Marichal (2002), \emph{Entropy of discrete Choquet capacities}, European
Journal of Operational Research, 3:137, 2002, pages 612-624.
I. Kojadinovic, J-L. Marichal and M. Roubens (2005), \emph{An axiomatic
approach to the definition of the entropy of a discrete Choquet
capacity}, Information Sciences 172, pages 131-153.
}
\seealso{
\code{\link{capacity-class}}, \cr \code{\link{Mobius.capacity-class}},
\cr \code{\link{card.capacity-class}}, \cr \code{\link{Mobius-methods}}.
}
\examples{
## a capacity
mu <- capacity(c(0,0,0:13))
## its M—bius transform
a <- Mobius(mu)
## their normalized entropy
entropy(mu)
entropy(a)
## similar examples with card.capacity objects
mu <- lower.capacity(4)
entropy(mu)
mu <- uniform.capacity(4)
entropy(mu)
}
\keyword{methods}
%\keyword{ ~~ other possible keyword(s)}