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1. Artificial Intelligence 39

In this case the problem only fuzzy sets are used for decision making which
makes the system to take decision like the human decision.
To design the fuzzy based system, the knowledge about the system
behavior is required to find the relationship between crisp value and the
fuzzy value (see above) and to frame the fuzzy base rule. This is the
drawback of the fuzzy based system when compared to ANN based system
which doesn’t require any knowledge about the system behavior.

5.4 Example

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 crisp –fuzzy relationship is as
mentioned in the section 5.2. The fuzzy base rule is as given in the table 1-1.
The values for the variables used in the section 5.2 are assumed as
mentioned in the table 1-2.

Table 1-2. Assumed values for the variables used in the section 5.2

X1 X2 X3 X4 Y1 Y2 Y3 Y4 Z1 Z2 Z3 Z4
3 5 7 10 20 45 65 100 35 70 90 100

For the arbitrary input crisp values xinput=6 and yinput=50, zout is obtained
as 78.8 using fuzzy logic system described in the section 5.2

Figure 1-20. Relationship between crisp value and fuzzy membership for the Input variable X
in the example