EIASC.m

function [y, yl, yr, l, r] = EIASC(Xl, Xr, Wl, Wr, needSort)
% EIASC: Enhanced Iterative Algorithm with Stopping Condition,
% <Comparison and practical implementation of type-reduction algorithms
% for type-2 fuzzy sets and systems>
% <A comprehensive study of the efficiency of type-reduction algorithms>
ly = length(Xl);
XrEmpty = isempty(Xr);
if XrEmpty
    Xr = Xl;
end
if max(Wl) == 0 || max(Wr) == 0
    yl = min(Xl);
    yr = max(Xr);
    y = (yl + yr) / 2;
    l = 1;
    r = ly - 1;
    return;
end
index = Wr == 0;
Xl(index) = [];
Xr(index) = [];
Wl(index) = [];
Wr(index) = [];
ly = length(Xl);
if nargin == 4
    needSort = 1;
end

% Compute yl
if needSort
    [Xl, index] = sort(Xl);
    Xr = Xr(index);
    Wl = Wl(index);
    Wr = Wr(index);
    Wl2 = Wl;
    Wr2 = Wr;
end
if ly == 1
    yl = Xl;
    l = 1;
else
    yl = Xl(end);
    l = 0;
    a = Xl * Wl';
    b = sum(Wl);
    while l < ly && yl > Xl(l+1)
        l = l + 1;
        t = Wr(l) - Wl(l);
        a = a + Xl(l) * t;
        b = b + t;
        yl = a / b;
    end
end

% Compute yr
if ~XrEmpty && needSort == 1
    [Xr, index] = sort(Xr);
    Wl = Wl2(index);
    Wr = Wr2(index);
end
if ly == 1
    yr = Xr;
    r = 1;
else
    r = ly;
    yr = Xr(1);
    a = Xr * Wl';
    b = sum(Wl);
    while r > 0 && yr < Xr(r)
        t = Wr(r) - Wl(r);
        a = a + Xr(r) * t;
        b = b + t;
        yr = a / b;
        r = r - 1;
    end
end
y = (yl + yr) / 2;