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

Question

Question

This question was previously asked in

UGC NET Computer Science (Paper 2) 07 Dec 2023 Official Paper

Answer 1

The correct answer is Crossover

Key Points

In fuzzy set theory, the term "crossover point" is used to refer to a point in the set where the membership function μA(x) equals to 0.5.
The membership function of a fuzzy set is a generalization of the indicator function in classical sets.
In a crisp set, the indicator function only gives values 0 (non-membership) or 1 (full membership).
However, in a fuzzy set, the membership function gives a degree of membership within the interval [0,1] and is allowed to take any value in this range.
A crossover point in the fuzzy set is essentially the point where degree of membership to the set is exactly 0.5, meaning that it's precisely in the middle ground between being fully in and fully out of the set.
The concept of the crossover point is part of why fuzzy logic is well-suited to handling uncertainty or ambiguity, since it allows for this sort of partial membership.