\HeaderA{fanny.object}{Fuzzy Analysis (FANNY) Object}{fanny.object}
\keyword{cluster}{fanny.object}
\begin{Description}\relax
The objects of class \code{"fanny"} represent a fuzzy clustering of a
dataset.
\end{Description}
\begin{Value}
A legitimate \code{fanny} object is a list with the following components:
\begin{ldescription}
\item[\code{membership}] matrix containing the memberships for each pair consisting of an
observation and a cluster.

\item[\code{memb.exp}] the membership exponent used in the fitting criterion.
\item[\code{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[\code{clustering}] the clustering vector of the nearest crisp clustering, see
\code{\LinkA{partition.object}{partition.object}}.
\item[\code{k.crisp}] integer (\eqn{\le k}{}) giving the number of \emph{crisp}
clusters; can be less than \eqn{k}{}, where it's recommended to
decrease \code{memb.exp}.
\item[\code{objective}] named vector containing the minimal value of the objective function
reached by the FANNY algorithm and the relative convergence
tolerance \code{tol} used.

\item[\code{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[\code{diss}] an object of class \code{"dissimilarity"}, see
\code{\LinkA{partition.object}{partition.object}}.
\item[\code{call}] generating call, see \code{\LinkA{partition.object}{partition.object}}.
\item[\code{silinfo}] list with silhouette information of the nearest crisp clustering, see
\code{\LinkA{partition.object}{partition.object}}.
\item[\code{data}] matrix, possibibly standardized, or NULL, see
\code{\LinkA{partition.object}{partition.object}}.
\end{ldescription}
\end{Value}
\begin{Section}{GENERATION}
These objects are returned from \code{\LinkA{fanny}{fanny}}.
\end{Section}
\begin{Section}{METHODS}
The \code{"fanny"} class has methods for the following generic functions:
\code{print}, \code{summary}.
\end{Section}
\begin{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.
\end{Section}
\begin{SeeAlso}\relax
\code{\LinkA{fanny}{fanny}}, \code{\LinkA{print.fanny}{print.fanny}},
\code{\LinkA{dissimilarity.object}{dissimilarity.object}},
\code{\LinkA{partition.object}{partition.object}}, \code{\LinkA{plot.partition}{plot.partition}}.
\end{SeeAlso}

