UGC NET CSE | December 2023 | Part 2 | Question: 38

Question

A _________ point of fuzzy set $\text{A}$ is a point $x \in \mathrm{X}$ at which $\mu \mathrm{A}(x)=0.5$

• A. Core
• B. Support
• C. Crossover
• D. $\alpha-$ cut

Answer 1

Answer: Crossover

A crossover point of a fuzzy set A is a point x in X where the membership value is exactly:

μA(x) = 0.5

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Explanation

In fuzzy set theory, each element has a membership value between 0 and 1. The crossover point represents the position where the element is equally belonging and not belonging to the set (i.e., uncertainty is maximum).

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Example

Let a fuzzy set A (e.g., “medium temperature”) be defined as:

A = {(20, 0.2), (25, 0.5), (30, 0.8)}

Here:

• μA(20) = 0.2 → not a crossover

• μA(25) = 0.5 → crossover point

• μA(30) = 0.8 → not a crossover

So, 25 is the crossover point of fuzzy set A.

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Note (for clarity)

• Core: where μA(x) = 1

• Support: where μA(x) > 0

• α-cut: set of elements with μA(x) >= α

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Final Answer

Crossover point