smf.m

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function y = smf(x, params)
%SMF S-shaped curve membership function.
%   SMF(X, PARAMS) returns a matrix which is the S-shaped
%   membership function evaluated at X. PARAMS = [X0 X1] is a 2-element
%   vector that determines the break points of this membership function.
%   When X0 < X1, SMF is a smooth transition from 0 (at X0) to 1 (at X1).
%   When X0 >= X1, SMF becomes a step function which jumps from 0 to 1
%   at (X0+X1)/2.
%   
%   For example:
%
%       x = 0:0.1:10;
%       subplot(311); plot(x, smf(x, [2 8]));
%       subplot(312); plot(x, smf(x, [4 6]));
%       subplot(313); plot(x, smf(x, [6 4]));
%       set(gcf, 'name', 'smf', 'numbertitle', 'off');
%
%   See also 
%       dsigmf, gauss2mf, gaussmf, gbellmf, evalmf, pimf, psigmf,
%       sigmf, trapmf, trimf, zmf, mf2mf

%   Roger Jang, 10-5-93, 7-14-94.
%   Copyright (c) 1994-98 by The MathWorks, Inc.
%   $Revision: 1.16 $  $Date: 1997/12/01 21:45:26 $

if nargin ~= 2,
    error('Two arguments are required by SMF.');
elseif length(params) < 2,
    error('SMF needs at least two parameters.');
end

x0 = params(1); x1 = params(2);

if x0 >= x1,
    y = x >= (x0+x1)/2;
    return;
end

y = zeros(size(x));

index1 = find(x <= x0);
if ~isempty(index1),
    y(index1) = zeros(size(index1));
end

index2 = find((x0 < x) & (x <= (x0+x1)/2));
if ~isempty(index2),
    y(index2) = 2*((x(index2)-x0)/(x1-x0)).^2;
end

index3 = find(((x0+x1)/2 < x) & (x <= x1));
if ~isempty(index3),
    y(index3) = 1-2*((x1-x(index3))/(x1-x0)).^2;
end

index4 = find(x1 <= x);
if ~isempty(index4),
    y(index4) = ones(size(index4));
end