# Q7(a) Fuzzy logic applications and complete controller example [10]

Subject: Intelligent Systems II

Exam: TEE

Reader: https://deep-learning-study-room.vercel.app/is2/#tee/papers/paper-2025-april/q7a

Canonical: https://deep-learning-study-room.vercel.app/read/is2/tee/papers/paper-2025-april--q7a/

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

**Question. Q7(a)** [10 marks · 2025-04-28]

List the applications of Fuzzy logic. Explain one in detail.

### Answer

**Fuzzy logic** represents gradual membership in linguistic categories and reasons with graded rules. A temperature can partly belong to both “warm” and “hot”; this is degree of membership, not a probability that a hidden label is true.

- Air-conditioning and automatic fan-speed control.
- Washing-machine adjustment of wash time, agitation or water use.
- Camera autofocus/exposure control.
- Vehicle and industrial process control.
- Decision support and multicriteria scoring when judgments are linguistic.
- Pattern recognition and fuzzy clustering.

### Detailed example: room-temperature fan controller

Swipe across the diagram to read its labels ↔

![Crisp measurements → fuzzification → rule evaluation → output aggregation/defuzzification → fan command. The rule base defines linguistic responses.](https://deep-learning-study-room.vercel.app/is2/fig/legacy25-controller.80f7bae29e.svg)

Diagram: Crisp measurements → fuzzification → rule evaluation → output aggregation/defuzzification → fan command. The rule base defines linguistic responses.. Labels: Fuzzy controller architecture | Sensors | temperature, occupancy | Fuzzification | membership degrees | Rule evaluation | IF–THEN strengths | Output calculation | one fan command | Membership functions + rule base define the controller | Mamdani: aggregated fuzzy area → centroid | Sugeno: weighted consequent values → crisp output

Crisp measurements → fuzzification → rule evaluation → output aggregation/defuzzification → fan command. The rule base defines linguistic responses.

| Block | Role in this example |
| --- | --- |
| Sensors / crisp input | Measure room temperature and occupancy |
| Fuzzifier | Convert each measurement to memberships such asCool, Warm, Hot andLow, High occupancy |
| Knowledge base | Store membership-function definitions and IF–THEN rules |
| Inference engine | Evaluate each rule's antecedent strength using the stated AND/OR operations |
| Defuzzifier / output computation | Convert the activated outputs to one fan command |
| Actuator | Apply the bounded fan-speed command; sensors provide fresh input for the next cycle |

### Illustrative rules and a transparent calculation

For a simple single-input numerical illustration, hold occupancy fixed. On 20≤T≤40°C chooseµWarm=(40−T)/20 andµHot=(T−20)/20. AtT=30°C both memberships are 0.5.

- IF temperature isWarm THEN fan command=50%.
- IF temperature isHot THEN fan command=90%.

Use a **zero-order Sugeno** design with these constant consequents, so its weighted output is:



$$
fan=\frac{0.5(50)+0.5(90)}{0.5+0.5}=\frac{25+45}{1}=70\%
$$



Here 50% and 90% are explicit illustrative output constants, not discovered from a source dataset. A Mamdani controller instead defines fuzzy output shapes and may use their aggregated centroid; the two procedures must not be mixed without saying which design is used.

### Advantages and limitations

- Smooth transitions avoid an abrupt full-speed jump at one fixed threshold.
- Rules are interpretable and can incorporate expert knowledge without requiring an exact plant equation.
- Membership functions and rules still require validation; poor design can create unsuitable or unstable behavior.
- More inputs and linguistic sets can make the rule base large. Safety limits and fallback behavior must be engineered separately.

Yaad rakho: measured number→kitnaWarm/Hot→rules→one usable fan command.