Question

4. 5 pts. Find and present graphically the output fuzzy set of a system with two inputs having two fuzzy sets per each input are represented in Figure 2 with one fuzzy output also defined in Figure 1, by applying the following four fuzzy rules: R?: IF $x_1$ is low AND $x_2$ is low, THEN y is low; R?: IF $x_1$ is low AND $x_2$ is high, THEN y is medium; R?: IF $x_1$ is zero AND $x_2$ is low, THEN y is medium; R?: IF $x_1$ is zero OR $x_2$ is high, THEN y is high. Assume that all fuzzy variables are normal (maxima of their membership functions are equal to 1). Each student should choose different values for the limits of the membership functions (left and right limits of the corresponding triangles) and selecct the actual crisp values for $x_1$ and $x_2$. Perform defuzzification of the system output using at least two different defuzzification methods. Hint: See Example 6.13 and its variant on page 36 of the class notes.

          4. 5 pts. Find and present graphically the output fuzzy set of a system with two inputs having
two fuzzy sets per each input are represented in Figure 2 with one fuzzy output also defined
in Figure 1, by applying the following four fuzzy rules:
R?: IF $x_1$ is low AND $x_2$ is low, THEN y is low;
R?: IF $x_1$ is low AND $x_2$ is high, THEN y is medium;
R?: IF $x_1$ is zero AND $x_2$ is low, THEN y is medium;
R?: IF $x_1$ is zero OR $x_2$ is high, THEN y is high.
Assume that all fuzzy variables are normal (maxima of their membership functions are
equal to 1). Each student should choose different values for the limits of the membership
functions (left and right limits of the corresponding triangles) and selecct the actual crisp
values for $x_1$ and $x_2$. Perform defuzzification of the system output using at least two
different defuzzification methods.
Hint: See Example 6.13 and its variant on page 36 of the class notes.

4. 5 pts. Find and present graphically the output fuzzy set of a system with two inputs having
two fuzzy sets per each input are represented in Figure 2 with one fuzzy output also defined
in Figure 1, by applying the following four fuzzy rules:
R?: IF x1 is low AND x2 is low, THEN y is low;
R?: IF x1 is low AND x2 is high, THEN y is medium;
R?: IF x1 is zero AND x2 is low, THEN y is medium;
R?: IF x1 is zero OR x2 is high, THEN y is high.
Assume that all fuzzy variables are normal (maxima of their membership functions are
equal to 1). Each student should choose different values for the limits of the membership
functions (left and right limits of the corresponding triangles) and selecct the actual crisp
values for x1 and x2. Perform defuzzification of the system output using at least two
different defuzzification methods.
Hint: See Example 6.13 and its variant on page 36 of the class notes.

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