l_mean.m

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

function meanv=L_mean(Lset)

% meanv=L_mean(Lset)
%
% The mean value of a fuzzy number in level-set representation.
%
% 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 mean value is defined as an interval whose bounds are upper and lower
% expectations. meanv=[a b]=[E^*(L_set) E_*(L_set)] with
% E^*(L_set) = \sum_{i=1}^nol (\alpha_i - \alpha_{i+1}) \sup Lset_{\alpha_i}
% E_*(L_set) = \sum_{i=1}^nol (\alpha_i - \alpha_{i+1}) \inf Lset_{\alpha_i}
% where \alpha_1 =1 > \alpha_2 > \ldots > \alpha_nol and \alpha_{nol+1}=0.
%
% 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

% 14 June 1996
% Last change: 20 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);

% dummy=[Lset(1,1); diff(Lset(:,1))];

dummy = flipud(diff(flipud([Lset(:,1);0])));

a=dummy'*Lset(:,2); % lower bound/expectation.

b=dummy'*Lset(:,3); % upper bound/expectation.

meanv = [a b];

if nargin==0 | nargout==0,
  x_max=Lset(nol,3);
  x_min=Lset(nol,2);
  from=x_min-(x_max-x_min)/100*10;
  to=x_max+(x_max-x_min)/100*10;

  plot_Lset(Lset,'y');
  %title('Mean value of a fuzzy number:');
  set(gca,'YTick',sort([Lset(:,1);0]));
  set(gca,'XTick',chop(sort([Lset(:,2);Lset(:,3)]),2));
  axis([from to 0 1.2]);grid 
  
  hold on
    % Draw line at left boundary:
    ord=linspace(0,1,10); abcis=a.*ones(1,10);
    line(abcis,ord,'Color','r'); plot(a,1,'r*');
    % Draw line for right boundary:
    ord=linspace(0,1,10); abcis=b.*ones(1,10);
    line(abcis,ord,'Color','r'); plot(b,1,'r*');
  hold off 
  xlabel(['Mean value = [',num2str(chop(a,3)),', ',num2str(chop(b,3)),']']);
end;