dis2alpha.m

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

function [alpha]=dis2alpha(univ, msf,qlevel)

% [alpha]=dis2alpha(univ, msf,qlevel)
%
% Discrete set to alpha-cut transformation of one fuzzy set.
% The discrete set, i.e univ and msf are assumed to be given
% as row vectors.
% univ   : the universe of discourse
% msf    : membership function of the fuzzy set
% qlevel : number of alpha levels in which the membership grade
%          is divided.
% alpha  : 3xqlevel matrix with qlevel sets in each column.
% 	   The first row contains the left boundary and the second
%          row contains the corresponding right-hand values of the
%          level. The third row contains the value alpha of the level.
%          The first column corresponds to the level alpha=1.
%
% FSTB - Fuzzy Systems Toolbox for MATLAB
% Copyright (c) 1993-1996 by Olaf Wolkenhauer
% Control Systems Centre at UMIST
% Manchester M60 1QD, UK
%
% O.Wolkenhauer 7 Feb 1996
% Last change   9 Feb 1996

% Test, if discrete set is normal, if not normalise:
dec=find(msf==1);
if isempty(dec),
  msf=modi_set(msf,'nor');
end;

for i=1:qlevel,                   % start with alpha=1.
  ulevel=1-(i-1)*(1/qlevel); % upper level of a section
  llevel=1-(i/qlevel);
  % Ensure via interpolation that appropriate values are excisting:
  ordv=[];
  for k=1:length(msf), % search from left to right
    if (msf(k) > llevel) & (msf(k) <= ulevel),
      msfalpha=interp1([msf(k) msf(1)],[univ(k) univ(1)],level);
      ordv=[ordv,msfalpha];
    end;
  end;
  alpha(1,i)=ordv(1);
  alpha(2,i)=ordv(length(ordv));
  alpha(3,i)=level;
end;