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\name{fanny.object}
\alias{fanny.object}
\title{Fuzzy Analysis (FANNY) Object}
\description{
The objects of class \code{"fanny"} represent a fuzzy clustering of a
dataset.
}
\section{GENERATION}{
These objects are returned from \code{\link{fanny}}.
}
\section{METHODS}{
The \code{"fanny"} class has methods for the following generic functions:
\code{print}, \code{summary}.
}
\section{INHERITANCE}{
The class \code{"fanny"} inherits from \code{"partition"}.
Therefore, the generic functions \code{plot} and \code{clusplot} can
be used on a \code{fanny} object.
}
\value{
A legitimate \code{fanny} object is a list with the following components:
\item{membership}{
matrix containing the memberships for each pair consisting of an
observation and a cluster.
}
\item{memb.exp}{the membership exponent used in the fitting criterion.}
\item{coeff}{
Dunn's partition coefficient \eqn{F(k)} of the clustering, where
\eqn{k} is the number of clusters. \eqn{F(k)} is the sum of all
\emph{squared} membership coefficients, divided by the number of
observations. Its value is between \eqn{1/k} and 1.
The normalized form of the coefficient is also given. It is defined
as \eqn{(F(k) - 1/k) / (1 - 1/k)}, and ranges between 0 and 1.
A low value of Dunn's coefficient indicates a very fuzzy clustering,
whereas a value close to 1 indicates a near-crisp clustering.
}
\item{clustering}{
the clustering vector of the nearest crisp clustering, see
\code{\link{partition.object}}.}
\item{k.crisp}{integer (\eqn{\le k}{<= k}) giving the number of \emph{crisp}
clusters; can be less than \eqn{k}, where it's recommended to
decrease \code{memb.exp}.}
\item{objective}{
named vector containing the minimal value of the objective function
reached by the FANNY algorithm and the relative convergence
tolerance \code{tol} used.% + still has 'iterations' for back-compatibility
}
\item{convergence}{
named vector with \code{iterations}, the number of iterations needed
and \code{converged} indicating if the algorithm converged (in
\code{maxit} iterations within convergence tolerance \code{tol}).
}
\item{diss}{
an object of class \code{"dissimilarity"}, see
\code{\link{partition.object}}.}
\item{call}{generating call, see \code{\link{partition.object}}.}
\item{silinfo}{
list with silhouette information of the nearest crisp clustering, see
\code{\link{partition.object}}.}
\item{data}{matrix, possibibly standardized, or NULL, see
\code{\link{partition.object}}.}
}
\seealso{
\code{\link{fanny}}, \code{\link{print.fanny}},
\code{\link{dissimilarity.object}},
\code{\link{partition.object}}, \code{\link{plot.partition}}.
}
\keyword{cluster}
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