modsuset.m

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

function [lib,c,areas] = modsuset(dec,range,no_of_sets,p1,p2)

% [lib,c,areas] = modsuset(dec,range,no_of_sets,p1,p2)
%
% Modeling of symetrical and unimodal trapezoidal fuzzy sets with the mouse.
% (Left mouse button picks points)
% One trapezoid around x=0 is defined by two characteristic points.
% The first point lies at x<0 (using the mouse) and y=0. The second point
% which has to be defined with the mouse lies at x<0 and y=1. The right (x>0)
% part of the triangle and all other library fuzzy sets are plotted auto-
% matically. 
% If the function is invoked without any parameters, you are ask for the 
% shape of the most positive and negative trapezoids and the x-range.
%
% For use with parameters: (no use of the mouse)
% dec = 'y' or 'n' indicating if open left/right trapecoids or not.
% Range is a POSITIVE NUMBER !. xfrom=-xto. 
% no_of_sets = number of sets in the library.
% p1,p2 are the characteristic points.
%
% lib is the library of fuzzy sets in the compact form. 4 characteristic 
% points describing a general trapecoid - one per collumn.
% c is a vector with the local FAM-rule centroids.
% areas is a vector with the area of the local FAM-rules.
%
% FSTB - Fuzzy Systems Toolbox for MATLAB
% Copyright (c) 1993-1996 by Olaf Wolkenhauer
% Control Systems Centre at UMIST
% Manchester M60 1QD, UK
%
%       20-April-1994

if nargin==0,
  disp('Symetrical unimodal fuzzy set library :')
  disp('Left mouse button picks points.')
  disp('Pick TWO characteristical points of a trapezoid; left from x=0.')
  dec=input('Open boundary (open left and right trapezoid) ? y/n [y]: ','s');
  if isempty(dec)
    dec='y';
  end;
  xrange(2)=abs(input('Universe of discourse. Domain space X +- : '));
  xrange(1)=-1*xrange(2);
  no_of_sets=input('Number of library subsets in the x-range (odd !): ');
else
  xrange(2)=range;
  xrange(1)=-1*xrange(2);
end;
clf; axis([xrange(1) xrange(2) 0 1.2]);
hold on; grid on
% the hole library is stored in a 4xno_of_sets matrix:
lib=zeros(4,no_of_sets); 
%  Each trapezoid in a collumn with the characteristic points.
y=zeros(4,no_of_sets); y(2,:)=ones(1,no_of_sets); 
y(3,:)=ones(1,no_of_sets);
but=1; mid=ceil(no_of_sets/2);            % button 1=left button.
if nargin==0,
 for co=1:2
    [xi,yi,but]=ginput(1);
    yi=round(yi);        
    plot(xi,yi,'go')
    lib(co,mid)=xi;
  end;
  hold off; 
else
  lib(1,mid)=p1;
  lib(2,mid)=p2;
end;
lib(3,mid)=abs(lib(2,mid));          % complete the half right to x=0.
lib(4,mid)=abs(lib(1,mid));
dist=xrange(2)/floor(no_of_sets/2);  % distance between the midpoints.
dis=dist;
for co=1:floor(no_of_sets/2),        % completing the library sets.
  lib(2,mid+co)=dis+lib(2,mid);      % start with positive x-range.
  lib(3,mid+co)=dis+lib(3,mid);
  lib(1,mid+co)=dis+lib(1,mid);
  lib(4,mid+co)=dis+lib(4,mid);
  dis=dis+dist;
end;
for co=1:floor(no_of_sets/2),        % negative x-range.
  lib(:,co)=(fliplr((-1.*lib(:,(no_of_sets+1)-co))'))';
end;
clf; 
if dec=='y',                         % open left/right trapezoids.
  lib(1,1)=-inf; lib(2,1)=(lib(3,1)+lib(2,1))/2;
  lib(4,no_of_sets)=inf; 
  lib(3,no_of_sets)=(lib(2,no_of_sets)+lib(3,no_of_sets))/2;
end; 
hold on;
plot_set(lib);
for co=1:no_of_sets,                 % determine the local centroids.
  c(co)=(lib(2,co)+lib(3,co))/2;
end;
for co=1:no_of_sets,                 % local area of general trapezoids.
areas(co)=0.5*(lib(2,co)-lib(1,co))+(lib(3,co)-lib(2,co))+0.5*(lib(4,co)-lib(3,co));
end;   
% Determine the overlap of two adjencent sets. (only for positive overlap
% values with sense)
% For symetrical unimodal trapezoids only once calculated.
alpha=atan(1/(lib(2,mid+1)-lib(1,mid+1)));
beta=atan(1/(lib(4,mid)-lib(3,mid)));
gamma=pi-alpha-beta; cl=lib(4,mid)-lib(1,mid+1);
al=(sin(alpha)*cl)/sin(gamma); bl=(sin(beta)*cl)/sin(gamma);
s=(al+bl+cl)/2; o=sqrt(s*(s-al)*(s-bl)*(s-cl)); % Heronic formula
overlap=['overlap = ',num2str(round(o*100/areas(mid))),'%'];
title(overlap);
xlabel('universe of discourse');
ylabel('membership');
grid on; hold off;