lr_mod.m

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

function [mu_M,X] = LR_mod(L,R,par,resX)

% [mu_M,X] = LR_mod(L,R,par,resX)
%
% Creating the membershipfunction of a LR-fuzzy set.
% par = [Xmin Xmax m n alpha beta mu_min mu_max] . 
% LR-fuzzy-set: the functions F=L and F=R are a reference function iff
% F(0)=1, F(x)=F(-x), F(x) is nonincreasing on [0,+inf), F(x) = 1 for x \in [-1,+1] and 0
% outside; F(x)=max(0,1-abs(x)^p), p>=0; F(x)=e^-abs(x)^p, p>=0; F(x)=1/(1+abs(x)^p), p>=0.
% A fuzzy number M is said to be an L-R type flat fuzzy number iff
%          L((m-x)/alpha) for x<=m
% mu_A(x)= 1              for m<x<n
%          R((x-n)/beta)  for x>=n
% For m=n M is a L-R type fuzzy number. L is for left and R for right reference. For m=n, m is
% the mean value of M, alpha and beta are called left and right spreads, respectively. A fuzzy
% number is denoted as: M=(m,n,alpha,beta)_LR .
% Examples:
% Trapezoid function : modlrset('tr','',[0,50,30,35,...],127)
% Triangular function: modlrset('tr','',[0,50,30,30,...],200) ( m1=m2 ! )
%
% The membershipfunction mu_M is discrete with the resolution resX.
% x contains the abscissa values.
%      ______
%     /      \         beta  is the distance between n and b.
% __a/ m    n \b___    alpha ------------ " -------- m and a.
%
 
% FSTB - Fuzzy Systems Toolbox
% Copyright (c) 1993-1996 by Olaf Wolkenhauer
% Control Systems Centre at UMIST
% Manchester M60 1QD, UK

%       28-Apr-1995
 
Xmin=par(1);
Xmax=par(2);
m=par(3);n=par(4);alpha=par(5);beta=par(6);
%mu_min=par(7);mu_max=par(8);

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

mu_M  = zeros(1,resX); 
X  = linspace(Xmin,Xmax,resX);  
for i=1:resX;
   mu_M(i)=LR_eval(L,R,[Xmin,Xmax,m,n,alpha,beta],X(i));
end;