A fuzzy logic controller evaluates water level in a tank. The linguistic…

1. The given problem uses fuzzy logic membership functions to determine the degree of membership of a crisp input value. The water level given is
   x = 32 cm.

2. First we evaluate the membership value for the Low function.

The membership function is defined as
μLow(x) = 1, for x ≤ 10
μLow(x) = (20 − x)/10, for 10 < x < 20
μLow(x) = 0, for x ≥ 20

Since x = 32 and 32 ≥ 20, it lies in the third condition.

Therefore
μLow(32) = 0

1. Next we evaluate the Medium membership function.

The function is defined as
μMedium(x) = 0, for x ≤ 15 or x ≥ 35
μMedium(x) = (x − 15)/5, for 15 < x < 20
μMedium(x) = 1, for 20 ≤ x ≤ 30
μMedium(x) = (35 − x)/5, for 30 < x < 35

Since 32 lies in the interval 30 < x < 35, we use the fourth expression.

μMedium(32) = (35 − 32)/5
μMedium(32) = 3/5
μMedium(32) = 0.6

1. Now we evaluate the High membership function.

The function is defined as
μHigh(x) = 0, for x ≤ 30
μHigh(x) = (x − 30)/10, for 30 < x < 40
μHigh(x) = 1, for x ≥ 40

Since 32 lies between 30 and 40:

μHigh(32) = (32 − 30)/10
μHigh(32) = 2/10
μHigh(32) = 0.2

1. Final membership values

μLow(32) = 0
μMedium(32) = 0.6
μHigh(32) = 0.2

1. Conclusion

The water level of 32 cm belongs mainly to the Medium category with membership 0.6 and partially to the High category with membership 0.2, while it does not belong to the Low category.