Intelligent Systems II · TEE · papers

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

Final / re-examination · 28 Apr 2025

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.
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.
BlockRole in this example
Sensors / crisp inputMeasure room temperature and occupancy
FuzzifierConvert each measurement to memberships such asCool, Warm, Hot andLow, High occupancy
Knowledge baseStore membership-function definitions and IF–THEN rules
Inference engineEvaluate each rule's antecedent strength using the stated AND/OR operations
Defuzzifier / output computationConvert the activated outputs to one fan command
ActuatorApply 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\%LaTeX: 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.