A _________ point of a fuzzy set A is a point x ∈ X at which µA (x) = 0.5

Answer: crossover

Explanation: A crossover point of a fuzzy set A is an element x in the universe X for which the membership function equals 0.5, i.e., μA(x) = 0.5. This term specifically names the points where membership is exactly one half.

• Core: the set of elements with full membership (μA(x) = 1).

• Support: the set of elements with nonzero membership (μA(x) > 0).

• α-cut: for a given α in [0,1], the α-cut is the set {x | μA(x) ≥ α} (sometimes a 'strong' α-cut is defined with strict >). Setting α = 0.5 yields the set of elements with membership at least 0.5, not the single term naming μA(x) = 0.5.

Quick example: If μA(x0) = 0.5, then x0 is a crossover point of A.