plot_set.m

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

function plot_set(xset,yset)

% plot_set(xset,yset)
%
% Plotting fuzzy sets.
% If no matrix yset with membershipvalues is passed, a normal set is 
% assumed. (ymin = 0 and ymax = 1) 
% Several setforms are possible: 
% Vector form - fully overlapping:
%   Each element of a 1*n vector describes the center (y=1) of a triangle.
%   (n triangles). Only one parameter is passed.
%   Each (crisp) input value is connected with two membership values.
%   xset should content at least two values. The abscissa-interval is 
%   restricted to +-1. All values outside this range get the membership 1.
% Compact general trapezoidal or matrix form:
%   Triangles and trapeziodal forms (open and closed) are possible.
%   There are no restrictions for the abscissa range. With a corresponding
%   set shape input values outside the interval get the membership 0.
%   If input values outside the range should get the membership 1, for the
%   most left and right points -inf and +inf respectively should be used.
%   xset is a 4*n matrix. The rows 1-4 correspond to the points P1..P4 
%   characterising a generel trapezoidal form from left to right. For
%   triangles P2 and P3 are equal.
%   In comparison to the form described above, dead zones are possible.
% Discrete form:
%   xset is a vector with the abscissa values.
%   yset is a mxn matrix with the n fit values of m subsets in each row.
% LR representation:
%   The first parameter xset is a matrix that contains the parameters of sets. 
%   [Xmin;Xmax;m;n;alpha;beta] (or without range: [m;n;alpha;beta]) for each 
%   set of the library in a row. 
%   The second parameter defines the shape function L(x)=R(x). 
%   For trapezoidal shape type 'tr' and "gaussian" shape 'ga' .
%   The sets are assumed to be normal. Xmin and Xmax must be the same for all
%   sets in the library. See LR_mod.m for more details.
%   Left or right open sets are described by alpha or beta equal to inf.
%
% FSTB - Fuzzy Systems Toolbox for MATLAB
% Copyright (c) 1993-1996 by Olaf Wolkenhauer
% Control Systems Centre at UMIST
% Manchester M60 1QD, UK
%
%       15-March-1994
%       revised 18 Jan 95
%	extended to fuzzy numbers in LR representation 13 Nov 95

[m,n]=size(xset); m2=[];
if nargin==2, [m2,n2]=size(yset); end;
if m==1 & nargin==1,                 % Sets nach Siler und Ying 1988.
  y=[1;1;0];
  x=[xset(1);xset(1);xset(2)];       % Triangle most left.
  for i=1:n-2;
    x=[x,[xset(i);xset(i+1);xset(i+2)]];
    y=[y,[0;1;0]];
  end;
  x=[x,[xset(n-1);xset(n);xset(n)]]; % Triangle most right.
  y=[y,[0;1;1]];
  if nargin==2,y=yset;end;
  plot(x,y);
  axis([xset(1),xset(n),0,1]);
  axis('auto');grid on;

elseif (m==4 & isempty(m2)) | (m==4 & m2==4),
  xmax=xset(4,n); xmin=xset(1,1);
  if nargin==1,
    y=ones(m,n); y(1,:)=zeros(1,n); y(4,:)=zeros(1,n);
    infs=[find(xset==-inf),find(xset==inf)];
    if ~isempty(infs),
      y(infs)=ones(size(infs));
    end;
  else
    y=yset;
  end;
  if xmax==inf,  xmax=xset(3,n);xset(4,n)=xset(3,n);end;
  if xmin==-inf, xmin=xset(2,1);xset(1,1)=xset(2,1);end;
  plot(xset,y);
  axis([xmin,xmax,0,1]);
  axis;grid on;

elseif (m==6 | m==4) & nargin==2 & isstr(yset),		% LR form of a fuzzy set.
  LRpar=xset;
  % left or right open sets are described by alpha or beta equal to inf :
  if ~isempty(find(LRpar==inf)),
    LRpar(find(LRpar==inf))=0.000001.*ones(length(find(LRpar==inf)),1);
  end;
  if (m==4 & n==2),	% find Umin Umax and add on to parameters :
    Umax = LRpar(2,n);
    Umin = LRpar(1,1);
  elseif (n==1),
    Umax = LRpar(2)+LRpar(4);
    Umin = LRpar(1)-LRpar(3);
    % Adding the range to the given matrices of sets:
    LRpar = [Umin.*ones(1,n); Umax.*ones(1,n); LRpar];
  end;  
  LRshape=yset;
  if strcmp(LRshape,'tr'),
    %LRshape = 'max(0,(1-abs(x)))';
    LRshape = 'max(0,(1-x))';
  elseif strcmp(LRshape,'ga'),
    LRshape = 'exp(-x.^2)';
  end;
 
  [yset,xset] = LR_mod(LRshape,LRshape,[LRpar(:,1)',0,1],200);
  [xset,yset] = stairs(xset,yset);
  for i=2:n,	% for each fuzzy set, with parameters in each collumn
    [y,x] = LR_mod(LRshape,LRshape,[LRpar(:,i)',0,1],200);
    [x,y] = stairs(x,y);
    yset = [yset,y];
  end;
  plot(xset,yset);
  axis([xset(1) xset(length(xset)) 0 1.2]);
  xlabel('universe of discourse'); ylabel('membership');
  grid on; axis;
   
elseif m==1 & nargin==2,           		% Discrete form. 
  [xsets,ysets]=stairs(xset,yset(1,:));
  for i=2:m2,
    [x,y]=stairs(xset,yset(i,:));
    ysets=[ysets,y];
  end;
  plot(xsets,ysets); 
  % plot(xset,yset);
  axis([xset(1) xset(n) 0 1.2]);
  xlabel('universe of discourse'); ylabel('membership');
  grid on; axis; 
end;