l_ng.m

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

function set = L_ng(Lset)

% set = L_ng(Lset)
%
% The fuzzy set of numbers that are necessarily greater than Q (represented
% by Lset). The membership function of SET equals the lower distribution 
% function of a fuzzy level set.
%
% The fuzzy quantity Lset is defined in terms of alpha-cuts (level sets).
% The first column defines the levels. The second and third column define 
% the alpha cut of the associated level.
% If invoked without lefthand arguments a plot is generated. If invoked without
% input parameters, an example is created.
%
% The left boundary of the level alpha=1, is interpolated - see file for
% details.
% 
% The third column of the return set contains Inf's to denote the right open
% set.
%
% Reference:
% D.Dubois and H.Prade
% "The Mean Value of a Fuzzy Number"
% Fuzzy Sets and Systems 24 (1987), pp.279-300.

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

% 20 June 1996
% Last change: 21 June 1996

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

nol=size(Lset,1); % the number of levels > 0.

set = Lset;
set(:,3) = Inf.*ones(nol,1);
 
set(2:nol,2) = flipud(Lset(2:nol,3));

% Previous calculation excludes the left boundary for the level
% alpha = 1 which would come from the intersection of the member-
% ship function of Lset with the ordinate. Since this intersection
% is not known precisly, we extrapolate this value:

set(1,2) = spline(Lset(:,1),Lset(:,3),0);

if nargin==0 | nargout==0,
  plot_Lset(Lset,'y');
  hold on
  plot_Lset(set,'r');
  hold off
end;