Fuzzy Review

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Fuzzy Review

• Winter 2005
• Lab 05/06 Lecture Supplement
• Feb 1, 2005

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Fuzzy Numbers

• Lets look at the crisp number 2 in fuzzy form
• It might look like this
• Why?
• 2 is 2 with precision 1
• numlt1 is 2 with precision 0
• numgt3 is 2 with precision 0
• 1ltnumlt2 is 2 with precision (num-1)
• 2ltnumlt3 is 2 with precision (3-num)

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Fuzzy Nums Arithmetic Ops

• Consider each monotonically increasing or
  decreasing section at a time
• Eg 21
• 3

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Fuzzy Set Logical Ops

• F2 fuzzy set with fuzzy number 2
• F1 fuzzy set with fuzzy number 1
• F2 n F1?
• F2 U F1?

5
Max-Min Inference

• Example
• cooling valve fuzzy system (2 fuzzy rules)
• Input a crisp value
• Output a crisp value
• Steps
• Input crisp value
• Fuzzification
• Inference
• Output set
• Defuzzification

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Cooling Valve Fuzzy System
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1) Input Crisp Value

• temp 18

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2) Fuzzification

• Read 18 off charts
• Chart 1 0.2
• Chart 2 0.5

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3) Inference

• Infer values of output rules

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4) Output Set

• We have 2 fuzzysets from previousstep
• Need to createsingle output set
• Use fuzzy OR /fuzzy union

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5) Defuzzification

• Determine crispvalue from outputchart
• Method CoG/A(center of gravity)or (center of
  area)
• Looking for anestimate (i.e. 70 inour example)

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Example Summary

• We had a fuzzy set with 2 fuzzy rules
• IF temp low THEN valve half open
• IF temp medium THEN valve almost open
• Input
• Temp 18
• Output
• Valve 70