l_sim.m

来自「FISMAT accommodates different arithmetic」· M 代码 · 共 80 行

function res=L_sim(s1,s2)

% res=L_sim(s1,s2)
%
% Similarity between Fuzzy Numbers, sim(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.
%
% 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 August 1996
% Last change: 7 August 1996
 
if nargin==0,
  %s1 = Trap2L([2.5 3 3 3.5],4);
  %s2 = Trap2L([4 4 4 5],4);
  
  s1 = Trap2L([1 2 2 3],4);
  s2 = s1;
end;

nol = size(s1,1);

distr = zeros(nol-1,2); % stores the distance measures for left and right for all levels.
distc = distr;

% Built matrix for the reference s1:
% The width of the level below the level considered is taken as 100 percent. Then the
% left and right distance of the considered level is calculated in percent.
for l=1:nol-1,
  distr(l,1) = (s1(l,2)-s1(l+1,2))/(s1(l+1,3)-s1(l+1,2));
  distr(l,2) = (s1(l+1,3)-s1(l,3))/(s1(l+1,3)-s1(l+1,2));
%  distr(l,1) = (s1(l,2)-s1(l+1,2));
%  distr(l,2) = (s1(l+1,3)-s1(l,3));
end;

% The same for s2 :
for l=1:nol-1,
  distc(l,1) = (s2(l,2)-s2(l+1,2))/(s2(l+1,3)-s2(l+1,2));
  distc(l,2) = (s2(l+1,3)-s2(l,3))/(s2(l+1,3)-s2(l+1,2));
%  distc(l,1) = (s2(l,2)-s2(l+1,2));
%  distc(l,2) = (s2(l+1,3)-s2(l,3));
end;

di = abs(distr(:)-distc(:));

% Average all the measures:
res = mean(di);
res = 1-res;

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(2,1,1),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('s1');
 
  subplot(2,1,2),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)]),2));
  axis([from to 0 1.2]);grid
  xlabel(['Shape similarity measure = ',num2str(res)]);
end;