A ________ point of fuzzy set A is a point \(x ε Χ\) at which μA(\(x\))=0.5
2023
A ________ point of fuzzy set A is a point \(x ε Χ\) at which μA(\(x\))=0.5
- A.
Core
- B.
Support
- C.
Crossover
- D.
\(\alpha - \)cut
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Correct answer: C
Answer: Crossover point
Definition: A crossover point of a fuzzy set A is a point x in X where μA(x) = 0.5.
Core: the set of points whose membership degree equals 1 (μA(x) = 1).
Support: the set of points with membership greater than 0 (μA(x) > 0).
Alpha-cut: for a chosen alpha, the alpha-cut is {x | μA(x) ≥ alpha}. If alpha = 0.5, the alpha-cut includes all points with μA(x) ≥ 0.5, which differs from the crossover points with μA(x) = 0.5 exactly.
Crossover point: the specific points where membership equals 0.5 (μA(x) = 0.5).
Why this is correct: the other terms refer to different threshold levels or sets (membership = 1, membership > 0, or membership ≥ alpha), whereas the crossover point refers exactly to membership = 0.5.