# Q4 · Fuzzy membership [3]

Subject: Intelligent Systems II

Exam: M2

Reader: https://deep-learning-study-room.vercel.app/is2/#m2/mocks/m2-paper-v2-2/q4

Canonical: https://deep-learning-study-room.vercel.app/read/is2/m2/mocks/m2-paper-v2-2--q4/

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.



$$
\mu_A(x)=\begin{cases}0,&x\le a\text{ or }x\ge c\\\dfrac{x-a}{b-a},&a<x\le b\\\dfrac{c-x}{c-b},&b<x<c\end{cases}
$$



#### 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



$$
\mu_A(32)=\frac{35-32}{35-25}=\frac{3}{10}=0.3
$$



##### Step 3. Interpret the value

The degree of belonging to A is 0.3. It is a membership degree, not a probability.

**Final answer.** μA(32) = 0.3.