https://github.com/cran/kappalab
Tip revision: d2fc5e4ce0f6c794342013b6dccb28fc6b39c9ba authored by Ivan Kojadinovic on 07 May 2005, 00:00:00 UTC
version 0.1-3
version 0.1-3
Tip revision: d2fc5e4
dual-methods.Rd
\name{dual-methods}
\docType{methods}
\alias{dual}
\alias{dual-methods}
\alias{dual,capacity-method}
\alias{dual,card.capacity-method}
\alias{dual,card.set.func-method}
\alias{dual,set.func-method}
\title{The dual (or conjugate) transform}
\description{Computes the dual (also called the \emph{conjugate}) of a set function. The
dual of the dual of a game gives the original game back.}
\section{Methods}{
\describe{
\item{object = "capacity" }{Returns an object of class \code{capacity}.}
\item{object = "card.capacity" }{Returns an object of class \code{card.capacity}.}
\item{object = "card.set.func" }{Returns an object of class \code{card.game}.}
\item{object = "set.func" }{Returns an object of class \code{game}. }
}}
\references{
T. Murofushi and M. Sugeno (2000), \emph{Fuzzy measures and fuzzy integrals},
in: M. Grabisch, T. Murofushi, and M. Sugeno Eds, Fuzzy Measures and
Integrals: Theory and Applications, Physica-Verlag, pages 3-41.
}
\seealso{
\code{\link{capacity-class}},
\cr \code{\link{card.capacity-class}},
\cr \code{\link{set.func-class}},
\cr \code{\link{card.set.func-class}}.
}
\examples{
## a game
mu <- game(c(0,-7:7))
mu
## its dual
dual(mu)
## and mu again
dual(dual(mu))
## a similar example with the upper capacity
mu <- capacity(c(0,rep(1,15)))
mu
dual(mu)
dual(dual(mu))
## a similar example with an object of class card.capacity
mu <- upper.capacity(6)
mu
dual(mu)
dual(dual(mu))
## the dual of a set function is a game
mu <- set.func(-7:8)
mu
dual(mu)
mu <- card.set.func(-2:5)
dual(mu)
}
\keyword{methods}
%\keyword{ ~~ other possible keyword(s)}