sider a fuzzy logic system where the input variable is “Temperature” ranging from 0°C to 50°C. The fuzzy sets for this variable are defined as “Cold”, “Warm”, and “Hot”. The membership function for the “Warm” set is a triangular function defined by the points (10,0),(25,1),(40,0), where the function increases linearly from 10°C to 25°C and decreases linearly from 25°C to 40°C. If the current temperature is 30°C, what is the membership value of the “Warm” set?
Question
sider a fuzzy logic system where the input variable is “Temperature” ranging from 0°C to 50°C. The fuzzy sets for this variable are defined as “Cold”, “Warm”, and “Hot”. The membership function for the “Warm” set is a triangular function defined by the points (10,0),(25,1),(40,0), where the function increases linearly from 10°C to 25°C and decreases linearly from 25°C to 40°C. If the current temperature is 30°C, what is the membership value of the “Warm” set?
Solution
To find the membership value of the "Warm" set when the temperature is 30°C, we need to use the decreasing part of the triangular membership function, which decreases linearly from 25°C to 40°C.
The slope of the decreasing part of the function can be calculated as follows:
Slope = (y2 - y1) / (x2 - x1) = (0 - 1) / (40 - 25) = -1 / 15
Then, to find the membership value at 30°C, we use the formula for a line:
y - y1 = slope * (x - x1)
Substituting the known values:
y - 1 = -1/15 * (30 - 25)
Solving for y gives:
y = 1 - (1/15 * 5) = 1 - 1/3 = 2/3
So, the membership value of the "Warm" set at 30°C is 2/3 or approximately 0.67.
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