# Q1(b) Membership function and age sketch [5]

Subject: Intelligent Systems II

Exam: TEE

Reader: https://deep-learning-study-room.vercel.app/is2/#tee/papers/paper-2024-final/q1b

Canonical: https://deep-learning-study-room.vercel.app/read/is2/tee/papers/paper-2024-final--q1b/

Actual historical paper ·100 marks attempted /140 offered · Q1 compulsory + any four of Q2–Q7. Source defects and solution assumptions are explicitly identified.

**Question. Q1(b)** [5 marks · 2024-04-17]

Define a membership function in the context of fuzzy logic. Using your intuition, sketch fuzzy membership functions for the “age of people”.

### Answer

A **membership function** assigns each element x of a universe X a degree μA(x) between 0 and 1, indicating compatibility with a linguistic concept A.



$$
\mu_A:X\rightarrow[0,1]
$$



A value of 0 means no membership, 1 means full membership, and intermediate values represent partial membership. This is a degree of a vague property, not automatically a probability of a random event.

Swipe across the diagram to read its labels ↔

![Illustrative age memberships, not universal demographic boundaries. An age can belong partly to two terms.](https://deep-learning-study-room.vercel.app/is2/fig/legacy24-age.140e92bbb3.svg)

Diagram: Illustrative age memberships, not universal demographic boundaries. An age can belong partly to two terms.. Labels: Illustrative age memberships, not universal demographic boundaries. An age can belong partly to two terms. | 0 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 0 | 0.25 | 0.5 | 0.75 | 1 | Young | Middle-aged | Old | μ(x)

Illustrative age memberships, not universal demographic boundaries. An age can belong partly to two terms.

| Term | One explicit assumed shape |
| --- | --- |
| Young | 1 until age 20; then decreases linearly to 0 at age 40. |
| Middle-aged | 0 up to 25; rises to 1 at 45; falls to 0 at 65. |
| Old | 0 up to 50; rises to 1 at 70; then remains 1. |

For age 35, μYoung=(40−35)/(40−20)=0.25 and μMiddle=(35−25)/(45−25)=0.5. The person is partly young and partly middle-aged. Overlap permits smooth decisions; a crisp boundary would abruptly change the label at one exact birthday.

**Remember:** membership = “kitna fit hota hai is label mein”. State the axis labels and the assumed age breakpoints when sketching.