moduldis.m

FISMAT accommodates different arithmetic operators, fuzzification and defuzzification algorithm, imp

function [ldf,udf] = moduldis(P)

%  [ldf,udf] = moduldis(P)
%
% Calculate upper and lower distribution function of the fuzzy set P:
% Upper distribution function:
%   \mu_{[P,+\infty)}(w) = \Pi_P((-\infty,w])=\sup_{u \leq w} \mu_P(u)
%   The set [P,+\infty) defines the numbers that can be greater than
%   or equal to the values of a variable associated with a fuzzy interval P.
% Lower distribution function:
%   \mu_{]P,+\infty)}(w) = Nec_P{((-\infty,w[) = \inf_{u \geq w}(1-\mu_P(u))
%    The set ]P,+\infty) is the set of numbers that are necessarily greater.
%
% The fuzzy interval P is given in a discrete format - row vector.
% udf, ldf are returned as row vectors.
%
% If invoked without lefthand argument, the set P and its lower and
% upper distribution is plotted.
% 
% Reference: 'Possibility Theory', D.Dubois & H.Prade, Plenum Press 1988
% 
% FSTB - Fuzzy Systems Toolbox for MATLAB
% Copyright (c) 1993-1996 by Olaf Wolkenhauer
% Control Systems Centre at UMIST
% Manchester M60 1QD, UK
%
% 21 Jan 1996
% Last change 22 Jan 1996

resu=length(P);
udf=zeros(1,resu); ldf=udf;
u=1:1:resu;
% \mu_{[P,+\infty)}(w) =
for w=1:resu,
  udf(w)=max(P(1:w));
end;
% \mu_{]P,+\infty)}(w) =
for w=1:resu,
  ldf(w)=min(1-P(w:resu));
end;
if nargout==0,
  plot_set(u,[P;ldf;udf]);
end;