Intelligent Systems II · M2 · mocks
Q4 · Fuzzy membership [3]
M2 mock 2 · 10 marks
Q1(a)+Q1(b) compulsory; any two of Q2–Q4. Answers immediately below each question.
Confirmed M2 pattern: Q1(a) [2] and Q1(b) [2] are compulsory. Attempt any two of Q2, Q3 and Q4, each worth 3 marks. The paper offers 13 marks; you attempt 10. These are newly written practice questions, not claims about the exact upcoming paper. Solutions are directly below each question; the teaching working is deliberately longer than a concise exam answer.
Q4. A fuzzy set A has triangular membership Tri(15, 25, 35). Find membership at x = 32. [3 marks · Practice]
Given
Left endpoint a = 15; peak b = 25; right endpoint c = 35; input x = 32.
To find
The membership degree μA(x), a number from 0 to 1.
Formula and why it applies
Locate x relative to a, b, c before choosing the branch.
LaTeX: \mu_A(x)=\begin{cases}0,&x\le a\text{ or }x\ge c\\\dfrac{x-a}{b-a},&a<x\le b\\\dfrac{c-x}{c-b},&b<x<c\end{cases}Solution
Step 1. Locate the input
25 < 32 < 35, so membership decreases as x moves away from the peak.
Step 2. Choose the correct expression
Falling side
LaTeX: \mu_A(32)=\frac{35-32}{35-25}=\frac{3}{10}=0.3Step 3. Interpret the value
The degree of belonging to A is 0.3. It is a membership degree, not a probability.