l_add.m

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

function res=L_add(s1,s2)

% res=L_add(s1,s2)
%
% Addition of Fuzzy Numbers, s1+s2, in level-set representation.
%
% s1 and s2 are fuzzy quantities 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:
% R.Kruse, J.Gebhardt, F.Klawonn:
% "Foundations of Fuzzy Systems"
% John Wiley & Sons, 1995

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

% 19 June 1996
% Last change: 20 June 1996
 
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 = size(s1,1);

res=s1;

for level=1:nol,
  res(level,2) = s1(level,2) + s2(level,2);
  res(level,3) = s1(level,3) + s2(level,3);
end; 

if nargin==0 | nargout==0,
  x_max=max(max(s1(nol,3),s2(nol,3)),res(nol,3));
  x_min=min(min(s1(nol,2),s2(nol,2)),res(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);res(:,2);res(:,3)]),2));
  axis([from to 0 1.2]);grid 
  ylabel('s1');
 
  subplot(3,1,2),plot_Lset(s2,'y');
  ylabel('s2');
  set(gca,'YTick',sort([s1(:,1);0]));
  set(gca,'XTick',chop(sort([s1(:,2);s1(:,3);s2(:,2);s2(:,3);res(:,2);res(:,3)]),2));
  axis([from to 0 1.2]);grid

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