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ACIT4620 - Computational Intelligence > Module 3 - Lecture 06-07 - Fuzzy sets/logic > Flashcards

Module 3 - Lecture 06-07 - Fuzzy sets/logic Flashcards

1
Q

Fuzzy sets and logic

What is an MF (membership function)?

A

A function that assigns a membership degree.

E.g. for any colour, how much does it belong to the set “red”?

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2
Q

Fuzzy sets and logic

What is MF short for?

A

Membership function

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3
Q

Fuzzy sets and logic

What is the difference between fuzzy sets and traditional sets?

A

Traditional sets are either 0 or 1, whereas fuzzy sets can be anything in-between. See image.

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4
Q

Fuzzy sets and logic

How are fuzzy sets expressed? (Set notation)

A

As a set of ordered pairs of x values and membership values. (See image)

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5
Q

Fuzzy sets and logic

What is mu in this image?

A

The membership function of A, which decided how much x belongs to A.

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6
Q

Fuzzy sets and logic

What is the symbol for the membership function?

A

See image.

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7
Q

Fuzzy sets and logic

Given the inputs in the image, what could the fuzzy set look like?

A

See image.

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8
Q

Fuzzy sets and logic

Given the inputs in the image, what could the fuzzy set look like?

A

See image.

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9
Q

Fuzzy sets and logic

What do plots of fuzzy sets look like? (Continuous and discrete)

A

See image

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10
Q

Fuzzy sets and logic

What region is the “crossover points” of a membership function?

A

See image

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11
Q

Fuzzy sets and logic

What region is the “alpha cuts” of a membership function?

A

See image

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12
Q

Fuzzy sets and logic

What region is the “support” of a membership function?

A

See image

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13
Q

Fuzzy sets and logic

What region is the “core” of a membership function?

A

See image

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14
Q

Fuzzy sets and logic

How do you write the subset operator?

A

See image

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15
Q

Fuzzy sets and logic

How do you write the complement operator?

A

See image

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16
Q

Fuzzy sets and logic

How do you write the union operator?

A

@ See image

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17
Q

Fuzzy sets and logic

@ How do you write the intersection operator?

A

See image

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18
Q

Fuzzy sets and logic

Describe subsets visually.

A

See image

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19
Q

Fuzzy sets and logic

Describe the NOT operation visually.

A

See image

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20
Q

Fuzzy sets and logic

Describe the AND operation visually.

A

See image

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21
Q

Fuzzy sets and logic

Describe the OR operation visually.

A

See image

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22
Q

Fuzzy sets and logic

What is the formula for the triangular MF?

A

See image

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23
Q

Fuzzy sets and logic

What is the formula for the trapezoidal MF?

A

See image

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24
Q

Fuzzy sets and logic

What is the formula for the gaussian MF?

A

See image

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25
Q

Fuzzy sets and logic

What is the formula for the generalized bell MF?

A

See image

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26
Q

Fuzzy sets and logic

What is the formula for the sigmoidal MF?

A

See image

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27
Q

Fuzzy sets and logic

How can you extend MFs?

A

E.g. by taking the product or absolute difference.

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28
Q

Fuzzy sets and logic

What does the triangular MF look like?

A

See image

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29
Q

Fuzzy sets and logic

What does the trapezoidal MF look like?

A

See image

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30
Q

Fuzzy sets and logic

What does the gaussian MF look like?

A

See image

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31
Q

Fuzzy sets and logic

What does the generalized bell MF look like?

A

See image

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32
Q

Fuzzy sets and logic

What is an L-R MF?

A

See image. An MF that is piecewise-defined.

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33
Q

Fuzzy sets and logic

What is an MF projection?

A

See image. Projection is when you have a multi-dimensional MF and project it down into a lower dimension.

34
Q

Fuzzy sets and logic

What is the formula for MF projection from a 2D MF down to X?

A

See image

35
Q

Fuzzy sets and logic

What are the two types of fuzzy complements?

A

Sugeno’s and Yager’s complement.

36
Q

Fuzzy sets and logic

What is the formula for Sugeno’s complement?

A

See image

37
Q

Fuzzy sets and logic

What is the formula for Yager’s complement?

A

See image

38
Q

Fuzzy sets and logic

What fuzzy complement is this formula? (See image)

A

Sugeno’s

39
Q

Fuzzy sets and logic

What fuzzy complement is this formula?

A

Yager’s

40
Q

Fuzzy sets and logic

What is the T-norm?

A

Fuzzy intersection

41
Q

Fuzzy sets and logic

What are some examples of T-norms? (MABD)

A

See image

42
Q

Fuzzy sets and logic

What are the monotonicity requirements for the T-norm?

A

See image

43
Q

Fuzzy sets and logic

What are the commutativity requirements for the T-norm?

A

See image

44
Q

Fuzzy sets and logic

What are the associativity requirements for the T-norm?

A

See image

45
Q

Fuzzy sets and logic

What are the boundary requirements for the T-norm?

A

See image

46
Q

Fuzzy sets and logic

What are the boundary requirements for the S-norm?

A

See image

47
Q

Fuzzy sets and logic

What are the monotonicity requirements for the S-norm?

A

See image

48
Q

Fuzzy sets and logic

What are the commutativity requirements for the S-norm?

A

See image

49
Q

Fuzzy sets and logic

What are the associativity requirements for the S-norm?

A

See image

50
Q

Fuzzy sets and logic

What law does the T- and S-norms satisfy?

A

DeMorgan’s laws

51
Q

Fuzzy sets and logic

T-Norm DeMorgan’s law:
What is the equivalent of T(a, b)?

A

See image

52
Q

Fuzzy sets and logic

S-Norm DeMorgan’s law:
What is the equivalent of S(a, b)?

A

See image

53
Q

Fuzzy sets and logic

Describe the extension principle

A

If A is a fuzzy set on X, you might want to create B = f(A).
then B = µ_B(x_i) / f(x_i)

(Since A = {( x, µ_A(x)) | x \in X}, you have access to x, but afterwards B = {( f(x), µ_B(x)) | x \in X})

54
Q

Fuzzy sets and logic

What’s the notation for a fuzzy relation?

A

See image

55
Q

Fuzzy sets and logic

What are some examples of fuzzy relations?

A

See image

56
Q

Fuzzy sets and logic

What is a linguistic variable?

A

A variable that can take linguistic values (words). E.g. Age is OLD.

57
Q

Fuzzy sets and logic

What’s the name of a variable like this: Age is OLD?

A

That’s a linguistic variable.

58
Q

Fuzzy sets and logic

What is a linguistic value?

A

It’s a fuzzy set.

59
Q

Fuzzy sets and logic

Are linguistic values fuzzy sets?

A

Yes

60
Q

Fuzzy sets and logic

Are linguistic variables fuzzy sets?

A

No

61
Q

Fuzzy sets and logic

What is a term set?

A

A term set is a collection of linguistic values.

62
Q

Fuzzy sets and logic

What is this an example of? (See image)

A

A term set

63
Q

Fuzzy sets and logic

Describe the difference between primary and composite linguistic values.

A

See image

64
Q

Fuzzy sets and logic

What are the operations on linguistic variables? (CDI)

A

See image

65
Q

Fuzzy sets and logic

What’s this an example of?
If the road is slippery, then driving is dangerous.

A

A fuzzy rule.

66
Q

Fuzzy sets and logic

What are fuzzy rules?

A

A set of rules on the form:
If X is A, then y is B.
If the road is slippery, then driving is dangerous.

67
Q

Fuzzy sets and logic

What are the two ways of interpreting fuzzy rules? (CE)

A

See image

68
Q

Fuzzy sets and logic

What does it mean when A is coupled with B?

A

See image

69
Q

Fuzzy sets and logic

What does it mean when A entails B?

A

See image

70
Q

Fuzzy sets and logic

What is this an example of? (See image)

A

A is coupled with B

71
Q

Fuzzy sets and logic

What is this an example of? (See image)

A

A entails B

72
Q

Fuzzy sets and logic

What’s the formula for fuzzy implication?

A

See image

73
Q

Fuzzy sets and logic

What is CRI short for?

A

Compositional rule of inference

74
Q

Fuzzy sets and logic

What is CRI (the compositional rule of inference)?

A

When you have x = a and some y = f(x), the CRI is how you find y = b.

75
Q

Fuzzy sets and logic

What is this an example of? (See image)

A

The compositional rule of inference.

76
Q

Fuzzy sets and logic

How do you write the complement of A? (As f(a))

A

N(a)

77
Q

Fuzzy sets and logic

How do you write Sugeno’s complement of A? (As f(a))

A

N_s(a)

78
Q

Fuzzy sets and logic

How do you write Yager’s complement of A? (as f(a))

A

N_w(a)

79
Q

Fuzzy sets and logic

What is the boundary requirement for the fuzzy complement?

A

N(0) = 1 and N(1) = 0

80
Q

Fuzzy sets and logic

What is the monotonicity requirement for the fuzzy complement?

A

N(a) > N(b) if a < b

81
Q

Fuzzy sets and logic

What is the involution requirement for the fuzzy complement?

A

N(N(a)) = a

ACIT4620 - Computational Intelligence (7 decks)

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