Page 44 - Algorithm Collections for Digital Signal Processing Applications using MATLAB

32 Chapter 1

B2(1,2)=B2(1,2)+ERR_HO(j,2)*lr_ho;
end
INDEX=[INDEX i];
SSE=[SSE sum(sum(ERR_HO.^2))];
plot(INDEX,SSE,'r');
xlabel('ITERATION')
ylabel('SSE')
pause(0.2)
end
H=logsig(INPUT*W1+repmat(B1,[8 1]));
OUTPUT=H*W2 +repmat(B2,[8 1]);
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logsiggv.m

function [res]=logsiggv(x)
res=1/(1+exp(-x));

5. FUZZY LOGIC SYSTEMS

Fuzzy is the set theory in which the elements of the set are associated with
fuzzy membership. Let us consider the set of days = {Sunday,
Monday, Tuesday, Wednesday, Thursday, Friday, and Saturday}. This is the
set in which elements belongs to the set with 100% membership.
Let us consider the set of rainy days ={Sunday (0.6), Monday (0.4),
Tuesday (0.4), Wednesday (0.6), Thursday (0.2), Friday (0.6), Saturday
(0.3)}. This is the set in which elements are associated with fuzzy
membership. Sunday (0.6) indicates that the Sunday belongs to the set of
rainy days with membership value 0.6. This is different from probability
assignment because in case of probability assignment, Sunday belongs to
non-rainy days with membership value 0.4. (ie) (1-0.6). But in case of fuzzy
sets Sunday belongs to non-rainy days with membership value of not
necessarily 0.4. It can be any value between 0 to 1.

5.1 Union and Intersection of Two Fuzzy Sets

Let us consider the example of computing union and intersection of fuzzy
sets as described below.

A={a (0.3), b (0.8), c (0.1), d (0.3)}

B={a (0.1), b (0.6), c (0.9), e (0-.1)}