What is the membership value for a triangular membership function with parameters a=1, b=5, and c=9 when x=7? 1.0 0.5 0.0 None of the above
Question
What is the membership value for a triangular membership function with parameters a=1, b=5, and c=9 when x=7? 1.0 0.5 0.0 None of the above
Solution 1
The triangular membership function is defined as:
μ(x) = max(min((x-a)/(b-a), (c-x)/(c-b)), 0)
where a, b, and c are the parameters of the function, and x is the input value.
Given a=1, b=5, c=9 and x=7, we can substitute these values into the function:
μ(7) = max(min((7-1)/(5-1), (9-7)/(9-5)), 0) = max(min(1.5, 1), 0) = max(1, 0) = 1
So, the membership value for a triangular membership function with parameters a=1, b=5, and c=9 when x=7 is 1.0.
Solution 2
The triangular membership function is defined as:
μ(x) = max(min((x-a)/(b-a), (c-x)/(c-b)), 0)
where a, b, and c are the parameters of the function, and x is the input value.
Given a=1, b=5, and c=9, and x=7, we can substitute these values into the function:
μ(7) = max(min((7-1)/(5-1), (9-7)/(9-5)), 0) = max(min(1.5, 1), 0) = max(1, 0) = 1
So, the membership value for a triangular membership function with parameters a=1, b=5, and c=9 when x=7 is 1.0.
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