Mamdani-Type Fuzzy Inference System, Slides of Artificial Intelligence

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Mamdani-Type

Fuzzy Inference

System

A sample of membership function

Fuzzy Logical Operations

Mamdani-Type Fuzzy Inference

Process

• (^) Mamdani-type fuzzy inference process consists of five steps
  • (^) Step 1: Fuzzify input variables
  • (^) Step 2: Apply fuzzy operator
  • (^) Step 3: Apply implication method
  • (^) Step 4: Apply aggregation method
  • (^) Step 5: Defuzzification

1- Fuzzify Input Variables

Fuzzifying input variable “temperature”

2- Apply Fuzzy Operator

Two different fuzzy sets of the antecedent in Rule 2 yielded the fuzzy membership values 0. 66 and 0.

respectively, and the maximum of the two values, 0.33, is picked out as the result of antecedent of Rule 2.

4- Apply Aggregati on Method

5- Defuzzification

Applying Centroid Method (also called center of area or center of gravity )

for defuzzification

where z is the output variable, and

𝜇𝐴 (𝑧) is the membership function ) is the membership function

of the aggregated fuzzy set A with

respect to z.

2. Determine Fuzzy Sets: Temperature Temp (^0 C). COLD COOL PLEASANT WARM HOT 0 Y* N N N N 5 Y Y N N N 10 N Y N N N 12.5 N Y* N N N 15 N Y N N N 17.5 N N Y* N N 20 N N N Y N 22.5 N N N Y* N 25 N N N Y N 27.5 N N N N Y 30 N N N N Y* Temp (^0 C). COLD COOL PLEASANT WARM HOT

Example: Air Conditioner

Temperature Fuzzy Sets

Temperature Degrees C

Truth Value

Cold

Cool

Pleasent

Warm

Hot

**0

1 0 5 10 15 20 25 30 Cold Cool Pleasent Warm Hot**

2. Determine Fuzzy Sets: Temperature

Example: Air Conditioner

Speed Fuzzy Sets

Speed

Truth Value

(^) MINIMAL SLOW MEDIUM FAST BLAST

2. Determine Fuzzy Sets: Fan Speed

Example: Air Conditioner

3. Elicit and construct fuzzy rules RULE 1: IF temp is cold THEN speed is minimal RULE 2: IF temp is cool THEN speed is slow RULE 3: IF temp is pleasant THEN speed is medium RULE 4: IF temp is warm THEN speed is fast RULE 5: IF temp is hot THEN speed is blast

Example: Air Conditioner

 COOL ( T ) = – T / 5 + 3.

 PLSNT ( T ) = T /2.5 - 6

Temp=16 COLD COOL PLEASANT WARM HOT 0 0.3 0.4 0 0

Example: Air Conditioner

• (^) Fuzzification
  • (^) Affected fuzzy sets: COOL and PLEASANT

Example: Air Conditioner

• (^) Inference RULE 1: IF temp is cold THEN speed is minimal RULE 2: IF temp is cool THEN speed is slow RULE 3: IF temp is pleasant THEN speed is medium RULE 4: IF temp is warm THEN speed is fast RULE 5: IF temp is hot THEN speed is blast