tprod.m

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

function inter=Tprod(s1,s2)

% inter=Tprod(s1,s2)
%
% T-norm product intersection operators between the two
% alpha level sets.
%
% The given sets and the returned set have the same levels.
%
% FSTB - Fuzzy Systems Toolbox for MATLAB
% Copyright (c) 1993-1996 by Olaf Wolkenhauer
% Control Systems Centre at UMIST
% Manchester M60 1QD, UK
%
% O.Wolkenhauer 20 June 1996
% Last change 20 June 1996
% Note: This function has not been tested properly.

if nargin==0,
  s1 = [1      1     1   ;
        0.75  0.75  1.25 ;
        0.5   0.5   1.5  ;
	0.25  0.25  1.75];

  s2 = [1      2     2   ;
        0.75  1.75  2.25 ;
        0.5   1.5   2.5  ;
	0.25  1.25  2.75];

  %s2=s1;
end;

[nol,c]=size(s1);

inter=s1;
inter(:,2:c) = NaN.*ones(nol,c-1);

for i=1:nol,
  % Find region in which the two cuts overlap:
  %    First check if they overlap at all:
  if ~(s1(i,3) < s2(i,2) | s2(i,3) < s1(i,2)),
    from = max(s1(i,2),s2(i,2)); % overlap left bound.
    to   = min(s1(i,3),s2(i,3)); % overlap right bound.

    level = s1(i,1) .* s2(i,1); 

    % Fit the calculated level into the given ones:
    indices = find(s1(:,1) <= level);
    if ~isempty(indices),
      inter(min(indices),2) = from;
      inter(min(indices),3) = to;
    end;
  else
    inter(i,2) = NaN;
    inter(i,3) = NaN;
  end;
end;

% Check for levels lower than alpha=1 which are filled with NaN.
% Set these levels equal to the level above;
for i=2:nol,
  if sum(isnan(inter(i,2:3))) == 2,
    inter(i,2:3) = inter(i-1,2:3);
  end;
end;

if nargin==0 | nargout==0,
  x_max=max(s1(nol,3),s2(nol,3));
  x_min=min(s1(nol,2),s2(nol,2));
  from=x_min-(x_max-x_min)/100*10;
  to=x_max+(x_max-x_min)/100*10;

  subplot(3,1,1),plot_Lset(s1,'y');
  title('Families of alpha-cuts:');
  set(gca,'YTick',sort([s1(:,1);0]));
  set(gca,'XTick',chop(sort([s1(:,2);s1(:,3);s2(:,2);s2(:,3)]),2));
  axis([from to 0 1.2]);grid 
  ylabel('set1 levels');
 
  subplot(3,1,2),plot_Lset(s2,'y');
  ylabel('set2 levels');
  set(gca,'YTick',sort([s1(:,1);0]));
  set(gca,'XTick',chop(sort([s1(:,2);s1(:,3);s2(:,2);s2(:,3)]),2));
  axis([from to 0 1.2]);grid

  subplot(3,1,3),plot_Lset(inter,'r');
  ylabel('Tprod');
  set(gca,'YTick',sort([s1(:,1);0]));
  set(gca,'XTick',chop(sort([s1(:,2);s1(:,3);s2(:,2);s2(:,3)]),2));
  xlabel('Universe of discourse');
  axis([from to 0 1.2]);grid
end;