Example $1$: Controlling a Washing Machine:

$1.$ Fuzzification:

Input variables: Clothes weight $($fuzzy sets: Light, Medium, Heavy$)$ Dirtiness level $($fuzzy sets: Clean, Slightly Dirty, Very Dirty$)$

Output variables: Water level $($fuzzy sets: Low, Medium, High$)$ Wash cycle duration $($fuzzy sets: Short, Medium, Long$)$

$2.$ Rule Evaluation:

Rules like: $"$IF Clothes weight is Heavy AND Dirtiness level is Very Dirty THEN Water level is High AND Wash cycle duration is Long"

$3.$ Aggregation:

Combine the outputs of multiple rules using fuzzy operators $($e$.$g$.,$ AND, OR$)$

$4.$ Defuzzification:

Convert fuzzy output sets $($e$.$g$.,$ High water level$)$ into a crisp value $($e$.$g$.,85$ liters$)$ using methods like centroid or mean of maxima.

Example $2$: Controlling a Traffic Signal:

$1.$ Fuzzification:

Input variables: Traffic density $($fuzzy sets: Low, Medium, High$)$ Time of day $($fuzzy sets: Day, Night$)$

Output variables: Green light duration $($fuzzy sets: Short, Medium, Long$)$ Red light duration $($fuzzy sets: Short, Medium, Long$)$

$2.$ Rule Evaluation:

Rules like: $"$IF Traffic density is High AND Time of day is Day THEN Green light duration is Short AND Red light duration is Long"

$3.$ Aggregation:

Combine outputs of rules using fuzzy operators.

$4.$ Defuzzification:

Convert fuzzy output sets into crisp values for signal timings.

Example $3$: Controlling a Robot's Movement:

$1.$ Fuzzification:

Input variables: Distance to obstacle $($fuzzy sets: Near, Far$)$ Obstacle size $($fuzzy sets: Small, Large$)$

Output variables: Speed $($fuzzy sets: Slow, Medium, Fast$)$ Direction $($fuzzy sets: Left, Right$)$

$2.$ Rule Evaluation:

Rules like: $"$IF Distance to obstacle is Near AND Obstacle size is Large THEN Speed is Slow AND Direction is Left"

$3.$ Aggregation:

Combine outputs of rules using fuzzy operators.

$4.$ Defuzzification:

Convert fuzzy output sets into crisp values for robot's movement.

Example $4$: Recommending Movies:

$1.$ Fuzzification:

Input variables: User's genre preferences $($fuzzy sets: Like, Dislike$)$ User's ratings of similar movies $($fuzzy sets: Low, Medium, High$)$

Output variables: Movie recommendation score $($fuzzy sets: Low, Medium, High$)$

$2.$ Rule Evaluation:

Rules like: $"$IF User likes Action movies AND has rated similar movies with High scores THEN Recommend Action movies with High scores"

$3.$ Aggregation:

Combine outputs of rules using fuzzy operators.

$4.$ Defuzzification:

Convert fuzzy output sets into crisp values for movie recommendations.