Fuzzy Sets and Logic

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Fuzzy Sets and Logic

• Sarah Spence Adams
• Discrete Mathematics

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Rethinking Regular Sets

• Universe U a, b, c, d, e, f, g, set S a,
  c, g
• We can define S by mapping each element of the
  universe to 0 or 1.
• If we map it to 1, it goes in S. Else, not in S.
• Here, f(a) 1, f(b) 0, f(c)1, f(d) 0, f(e)
  0, f(f) 0, f(g) 1.

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Fuzzy Sets

• Every element in a fuzzy set S has a degree of
  membership
• Map each element of U to a value within the
  interval 0, 1
• S 0.6 a, 0.3 c, 0.9 g
• c has 0.3 degree of membership in S

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Fuzzy Logic

• This business of having degrees of membership
  rather than in or out
• Truth values are between true and false
• Introduced in 1965 to model uncertainty in
  natural language tall, fair, nice, large, hot

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Why use fuzzy logic?

• PROS
• Used to solve highly complex problems where math
  modeling is too difficult/impossible
• Tolerant of imprecise data
• Approximation can model arbitrary nonlinear
  functions
• Intuitive, based on linguistic terms
• Convenient way to express expert and common sense
  knowledge

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Why use fuzzy logic?

• Cons
• Not a cure for all
• Crisp/precise models can be more efficient and
  even convenient
• Other approaches might be formally verified to
  work

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Apply to Computer Games

• Can have different characteristics of players
• Strength strong, medium, weak
• Aggressiveness meek, medium, nasty
• If meek and attacked, run away fast
• If medium and attacked, run away slowly
• If nasty and strong and attacked, attack back
• Control of a vehicle
• Should slow down when close to car in front
• Should speed up when far behind car in front
• Provides smoother transitions, no sharp boundary

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Other Applications

• compensation against vibrations in camcorders
• home appliances (washing machines, dish washers,
  rice cookers, etc.)
• recognition of handwriting, objects, voice
• image processing
• flight aid for helicopters
• simulation for legal proceedings
• improvement of fuel-consumption for automobiles
• early recognition of earthquakes
• and in almost any other field you can think of

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Sound interesting?

• Its never to early to start thinking about
  course project topics!