% FuzzyTest.m
%
% Exercise functions associated with fuzzy logic:
%  m = FuzzyMembership(membership_left_center_right_pts, x)
%  m_AND = FuzzyAND(m_array)
%  c = FuzzyCentroid(m)

membership_left_center_right_pts = ...
  [0.5, 1.0,  1.5];

% Specify x values.
x_pts = 0:0.1:2;

% Calculate membership values for membership function
m_vec = FuzzyMembership(membership_left_center_right_pts, x_pts);

% Plot the membership function.
figure(1)
plot(x_pts, m_vec, 'b-')
set(gcf,'color','white')
xlabel('x')
ylabel('membership')
title('Fuzzy membership function')


% Create mesh for plot of fuzzy AND.
x1_limits = [0, 2];     % [min, max] for x1.
x2_limits = [0, 2];     % [min, max] for x2.
num_pts_x1_and_x2 = 51;  % number of pts in both x1 and x2 directions.

% Create the x1,x2 pts.
x1_spacing = (x1_limits(2)-x1_limits(1))/(num_pts_x1_and_x2 - 1);
x2_spacing = (x2_limits(2)-x2_limits(1))/(num_pts_x1_and_x2 - 1);
x1 = x1_limits(1) : x1_spacing : x1_limits(2);
x2 = x2_limits(1) : x2_spacing : x2_limits(2);
[xx1,xx2] = meshgrid(x1,x2);

% Calculate fuzzy_AND of membership of pts on grid
for x1_index = 1:size(xx1,1)
  for x2_index = 1:size(xx2,2)
    m1 = FuzzyMembership(membership_left_center_right_pts, ...
                         xx1(x1_index,x2_index));
    m2 = FuzzyMembership(membership_left_center_right_pts, ...
                         xx2(x1_index,x2_index));
    m_AND(x1_index,x2_index) = FuzzyAND([m1, m2]);
  end
end

% Plot the surface.
figure(2)
surf(xx1,xx2,m_AND)
set(gcf,'color','white')
xlabel('x1')
ylabel('x2')
zlabel('Fuzzy AND')
title('Fuzzy AND function of membership functions')


% Calculate centroids of memberships of pts on grid
c_array = FuzzyCentroid(m_AND);

% Plot the surface.
figure(3)
surf(xx1,xx2,c_array)
set(gcf,'color','white')
xlabel('x1')
ylabel('x2')
zlabel('Centroid value')
title('Centroid value of fuzzy membership values')