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1. Artificial Intelligence 33

The elements of the set AUB are the unique elements collected from both
the sets A and B. The membership value associated with the elements of the
set AUB is the maximum of the corresponding membership values collected
from the set A and B.

Thus AUB = {a (0.3), b (0.8), c (0.9), d (0.3), e (0.1)}

Similarly the elements of the set A∩B are the common elements
collected from the sets A and B. The membership value associated with the
elements of the set AUB is the minimum of the corresponding membership
values collected from the set A and B.

Thus A∩B= {a (0.1), b (0.6), c (0.1)}

5.2 Fuzzy Logic Systems

Let us consider the problem of obtaining the optimum value of the
variable ‘Z’ obtained as the output of the fuzzy logic system decided by the
values of the variable ‘X’ and ‘Y’ taken as the input to the fuzzy logic
system using fuzzy logic algorithm.
The values of the variable ‘X’ vary from X min to X max. Actual value of
the variable is called crisp value. The group of the values ranges from X min to
X max is grouped into 3 sets XSMALL, XMEDIUM, XLARGE. The
relationship between the crisp value and fuzzy membership value is given in
the figure 1-13.

Figure 1-13. Fuzzy system