l_abs.m

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

function res=L_abs(Lset)

% res=L_abs(Lset)
%
% Absolute value of the fuzzy quantity Lset in level-set representation.
%
% The fuzzy quantity Lset is defined in terms of alpha-cuts (level sets).
% The first column of both s1 and s2 define the levels that are required to be
% equal. The second and third column define the alpha cut of the associated level.
% In consequence only convex fuzzy quantities are allowed.
%
% If invoked without lefthand arguments a plot is generated. If invoked without
% input parameters, an example is created.
%
% Reference:
% D.Dubois, H.Prade:
% "Possibility Theory"
% Plenum Press, 1986

% FSTB - Fuzzy Systems Toolbox for MATLAB
% Copyright (c) 1993-1996 by Olaf Wolkenhauer
% Control Systems Centre at UMIST
% Manchester M60 1QD, UK

% 6 August 1996
% Last change: 6 August 1996
 
if nargin==0,
  %Lset = Trap2L([0 1 1 3],4);    % should stay the same.
  %Lset = Trap2L([-3 -1 -1 0],4); % should give -Q.
  %Lset = Trap2L([-2 0 0 1],4);   % only positive half of -Q.
  Lset = Trap2L([-3 1 1 4],4);    % example where union of Q and -Q has a gap.
end;

nol = size(Lset,1);

res=Lset;
dummy=Lset;

% Determine the negation of Q:
for level=1:nol,
  res(level,2) = -1*Lset(level,3);
  res(level,3) = -1*Lset(level,2);
end;

gapflag = 0;

% Form the union of Q and -Q:
for level=1:nol,
  if (res(level,3) <= Lset(level,2)),         % there is a gap : -Q is left to Q.
    dummy(level,2) = Lset(level,2);
    dummy(level,3) = Lset(level,3);
  elseif (Lset(level,3) <= res(level,2)),     % there is a gap :  Q is left to -Q.
    dummy(level,2) = res(level,2);
    dummy(level,3) = res(level,3);
  else,
    dummy(level,2) = min(res(level,2),Lset(level,2));
    dummy(level,3) = max(res(level,3),Lset(level,3));
  end;
end;
% Take the intersection of Q \cup -1 and [0, -\infty):
for level=1:nol,
  res(level,2) = max(0,dummy(level,2));
  res(level,3) = max(0,dummy(level,3));
end; 

if nargin==0 | nargout==0,
  x_max=max(Lset(nol,3),res(nol,3));
  x_min=min(Lset(nol,2),res(nol,2));
  from=x_min-(x_max-x_min)/100*10;
  to=x_max+(x_max-x_min)/100*10;

  subplot(2,1,1),plot_Lset(Lset,'y');
  title('Families of alpha-cuts:');
  set(gca,'YTick',sort([Lset(:,1);0]));
  set(gca,'XTick',chop(sort([Lset(:,2);Lset(:,3);res(:,2);res(:,3)]),2));
  axis([from to 0 1.2]);grid 
  ylabel('Q');
 
  subplot(2,1,2),plot_Lset(res,'r');
  ylabel('abs(Q)');
  set(gca,'YTick',sort([Lset(:,1);0]));
  set(gca,'XTick',chop(sort([Lset(:,2);Lset(:,3);res(:,2);res(:,3)]),2));
  xlabel('Universe of discourse');
  axis([from to 0 1.2]);grid
end;