modlrset.m

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

function [f,x] = modlrset(L,R,par,resx)

% [f,x] = modlrset(L,R,par,resx)
%
% Creating the membershipfunction of a LR-fuzzy set.
% par = [xmin xmax m1 m2 alpha beta ymin ymax] . 
% LR-fuzzy-set: the functions L and R must have the following 
% characteristic:
% F(0)=0, F(x)<1 fuer alle x>0, F(x)>0 fuer alle x<1, F(x)=F-x).
%       L((m1-x)/alpha) for x<m1
% F(x)= 1               for m1<=x<=m2
%       R((x-m2)/beta)  for x>m2
% Examples are F(x)=e^-x, F(x)=1/(1+x^2), F(x)=max(0,1-x^p)
% Trapezoid function : modlrset('tr','',[0,50,30,35,...],127)
% Triangular function: modlrset('tr','',[0,50,30,30,...],200) ( m1=m2 ! )
%
% The membershipfunction f is discrete with the resolution resx.
% x contains the abscissa values.
%       ______
%      /      \          beta  is the distance between m2 and b.
% __a/ m1    m2 \b___    alpha ------------ " -------- m1 and a.
%
%
% FSTB - Fuzzy Systems Toolbox for MATLAB
% Copyright (c) 1993-1996 by Olaf Wolkenhauer
% Control Systems Centre at UMIST
% Manchester M60 1QD, UK
%
%       25-Feb-1994

xmin=par(1);
xmax=par(2);
m1=par(3);m2=par(4);alpha=par(5);beta=par(6);ymin=par(7);ymax=par(8);

if all(L(1:2)=='tr')
  L='max(0,(1-x))'; R=L;
end;

f  = zeros(1,resx); 
dy = ymax-ymin; 
if (xmin==xmax) 
  o = f;
  o(:) = xmin;
else 
  o  = linspace(xmin,xmax,resx);  
end
for i=1:resx;
  if (o(i) >= m1) & (o(i) <= m2); f(i)=ymax; end;
%  if (o(i) <  m1); x=(m1-o(i))/(alpha+1e-6); f(i)=ymin+dy*eval(L); end;
%  if (o(i) >  m2); x=(o(i)-m2)/(beta+1e-6);  f(i)=ymin+dy*eval(R); end;
  if (o(i) <  m1); x=(m1-o(i))/(alpha+1e-6); f(i)=ymin+dy*max(0,1-x); end;
  if (o(i) >  m2); x=(o(i)-m2)/(beta+1e-6);  f(i)=ymin+dy*max(0,1-x); end;
end;
x=o;