probabilistic OR (also known as the algebraic sum) of the columns in
y = probor(
Within the fuzzy inference process, the
probor function is used as
either a fuzzy operator when evaluating rule antecedents or an aggregation operator when
combining the output fuzzy sets from all the rules.
Compute Probabilistic OR Between Two Membership Functions
Define the universe of discourse (input values) for the membership functions.
x = 0:0.1:10;
Define two Gaussian membership functions with different means and variances.
y1 = gaussmf(x,[0.5 4]); y2 = gaussmf(x,[2 7]);
Compute the probabilistic OR between these membership functions.
y = probor([y1;y2]);
Plot the results.
plot(x,[y1;y2;y]) legend('y1','y2','y') ylim([-0.05 1.05]) ylabel('Membership') xlabel('Input Value')
x — Fuzzy input values
array | row vector
Fuzzy input values, specified as an array or a row vector.
y — Probabilistic OR values
Probabilistic OR values, returned as a row vector with the same number of columns as
x. Each element of
y contains the
probabilistic OR value for the corresponding column in
x has one row, then
x = [A;B], where
are row vectors, then the
ith element of
the following algebraic sum.
y(i) = A(i) + B(i) - A(i)*B(i);
x has more than two rows, the probabilistic OR is calculated
for the first two rows. Then, the probabilistic OR is computed between the result and
the next row. This process repeats for each subsequent row.
x = [A;B;C;D] y(i) = A(i) + B(i) - A(i)*B(i); y(i) = y(i) + C(i) - y(i)*C(i); y(i) = y(i) + D(i) - y(i)*D(i);