Understanding

Fuzzy Logic

Evan Prodromou

Fuzzy.ai

What... is it?
How... does it work?
Why... would I use it?

Fuzzy Logic

  • The Logic ... (explicit rules defined by humans)
  • ... of Fuzzy sets ... (group membership is not clear-cut)
  • ... that can be optimized (improved with usage)

Fuzzy sets

  • Have degrees of membership (0.0 -> 1.0)
  • Represent vague terms from the real world
  • Can overlap

Fuzzy sets

1.0

1.0

0.0

0.0

Membership

0

Membership

10

20

30

40

50

60

70

80

"Young"

"Old"

Age (in years)

Another fuzzy set

1.0

1.0

0.0

0.0

Membership

0

Membership

10

20

30

40

"Low"

"High"

Savings rate (percentage of income)

Fuzzy logic

  • Rules statements
  • About fuzzy sets
  • Implications between them

IF Age IS Young THEN Savings Rate IS High.

IF Age IS Old THEN Savings Rate IS Low.

Notes about rules

  • "Then" part fires proportionate to the "If" part
  • Multiple rules can fire for the same input
  • Many inputs can be used (e.g., income, # of children)
  • Rules can be weighted (some rules are more important)

IF Age is Young AND Number of Children is Low Then Savings Rate is High.

IF Age is Old OR Income is Low Then Savings Rate is Low.

IF NOT Number of Children is Low Then Savings Rate is Low.

Optimization

  • Improve the parameters to give better results
  • Direct results ("That's not the right savings rate!")
  • Indirect results ("I had enough savings to buy a boat!")

Why use it?

  • When explicit rules matter, but you want optimization, too
  • When there is a lot of organizational knowledge
  • When you don't have a lot of training data for a pure learning system
  • When terms in the problem domain are vague

Understanding Fuzzy Logic

By Evan Prodromou

Understanding Fuzzy Logic

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