

   FFuuzzzzyy CCooddiinngg ((33--WWaayy))

        flou(a)

   AArrgguummeennttss::

          a: real-valued vector, with no missing values.

   DDeessccrriippttiioonn::

        Simple fuzzy, or piecewise linear, coding of a vector:
        each value in the vector is replaced by a 1 (if it is
        above or equal to the 67th quantile), by a 0 (if it is
        below or equal to the 33rd quantile), and by a linearly
        interpolated value between 0 and 1 (if it lies between
        the 33rd and 67th quantiles).

   VVaalluuee::

        matrix of `length(a)' rows, and two columns.  The first
        column contains the fuzzily coded values of `a', and
        the second column contains their complements.  Hence
        each row of this returned matrix necessarily sums to 1.

   BBAACCKKGGRROOUUNNDD::

        This form of coding is suitable for a subsequent corre-
        spondence analysis.  When all variable have been
        fuzzily (or logically) coded, the row masses (propor-
        tional to the row sums) are identical.

   RReeffeerreenncceess::

        J.-P. Benzecri Correspondence Analysis Handbook Marcel
        Dekker, Basel, 1992.

        F.J. Gallego, Codage flou en analyse des correspon-
        dances, Les Cahiers de l'Analyse des Donnees vol. VII,
        413-430, 1982

   SSeeee AAllssoo::

        `logique', `ca', `supplr', `supplc'.

   EExxaammpplleess::

        # Fuzzy coding of input variables, `a', `b', `c':
        a.fuzz <- flou(a)
        b.fuzz <- flou(b)
        c.fuzz <- flou(c)
        newdata <- cbind(a.fuzz, b.fuzz, c.fuzz)
        ca.newdata <- ca(newdata)

