Module 3 - Lecture 08 - Fuzzy Systems

Question 1

Fuzzy systems

What are some advantages of fuzzy modelling?

Answer 1

HFPLIS

• Models based on human approximate reasoning
  Models are:
• faster
• good in practice (Good performance)
• linguistic
• interpretable (no black boxes)
• simpler

Question 2

Fuzzy systems

What is a rule base?

Answer 2

A collection of fuzzy rules

Question 3

Fuzzy systems

What do you call the collection of fuzzy rules in a fuzzy inference system?

Answer 3

A rule base

Question 4

Fuzzy systems

What is the basic structure of a fuzzy inference system? (RDI)

Answer 4

• Rule base
• Database of linguistic values for the fuzzy rules
• Fuzzy reasoning engine (inference engine)

Question 5

Fuzzy systems

What are the 3 steps in a FIS (Fuzzy inference system)? (FID)

Answer 5

• Fuzzification
• Fuzzy Inference
• Defuzzification

Question 6

Fuzzy systems

What input format does a FIS take?

Answer 6

Either crisp values or fuzzy values.

Question 7

Fuzzy systems

What is a crisp value?

Answer 7

Traditional values, data without MFs.

Question 8

Fuzzy systems

What do you call an input/output value that’s not fuzzy?

Answer 8

Crisp

Question 9

Fuzzy systems

What is FIS short for?

Answer 9

Fuzzy inference system

Question 10

Fuzzy systems

What input types can the Mamdani system take?

Answer 10

Either fuzzy or crisp.

Question 11

Fuzzy systems

What do you need to do if the input is crisp?

Answer 11

Fuzzification of the input.

Question 12

Fuzzy systems

What is the basic FIS?

Answer 12

Mamdani type.

Question 13

Fuzzy systems

What’s a synonym for the Mamdani FIS type?

Answer 13

Basic FIS.

Question 14

Fuzzy systems

What does defuzzification do?

Answer 14

It transforms fuzzy outputs to crisp values.

Question 15

Fuzzy systems

In a Mamdani FIS, what T-norm is used?

Answer 15

T-norm operator: min / algebra product

Question 16

Fuzzy systems

In a Mamdani FIS, what S-norm is used?

Answer 16

S-norm operator: max / sum

Question 17

Fuzzy systems

In a Mamdani FIS, what is the Fuzzy implication? (What functions)

Answer 17

Fuzzy implication: Sum-product / max-min composition

Question 18

Fuzzy systems

How do you fuzzify the input value of 70 (x) in the image?

Answer 18

Read the values y = f(x) fro the graph and put them into a vector.

Question 19

Fuzzy systems

In the attached image, where are the T-norm and S-norm, respectively?

Answer 19

See image

Question 20

Fuzzy systems

What is the “centre of gravity” method an example of?

Answer 20

A defuzzification method.

Question 21

Fuzzy systems

What is the formula for the “centre of gravity” method?

Answer 21

See image.

Question 22

Fuzzy systems

What is the formula for the “bisector of area” method?

Answer 22

See image

Question 23

Fuzzy systems

What is the formula for the “mean of maximum” method?

Answer 23

See image

Question 24

Fuzzy systems

What is the formula for calculating z in Sugeno type?

Answer 24

If x is A and y is B, then z = f (x, y)

Question 25

# Fuzzy systems In a Sugeno type FIS, we have If x is A and y is B, then z = f (x, y). What are A and B called?

Answer 25

The antecedents

Question 26

# Fuzzy systems In a Sugeno type FIS, we have If x is A and y is B, then z = f (x, y). Where is the antecedent(s)?

Answer 26

A and B are antecedents.

Question 27

# Fuzzy systems In a Sugeno type FIS, we have If x is A and y is B, then z = f (x, y). What is z = f (x, y) called?

Answer 27

The consequent.

Question 28

# Fuzzy systems In a Sugeno type FIS, we have If x is A and y is B, then z = f (x, y). Where is the consequent(s)?

Answer 28

z = f (x, y) is the consequent.

Question 29

# Fuzzy systems In a Sugeno-type model with z = f(x, y), what is the function f(x, y)?

Answer 29

Usually, a polynomial of x and y. E.g: - Zero-order: z = f(x, y) = 3 - First-order: z = f(x, y) = 3x + 2y +3

Question 30

# Fuzzy systems In this rule example, what is the consequent and what is the antecedent? If height is tall, then weight is fairly heavy.

Answer 30

Antecedent: If height is tall Consequent: then weight is fairly heavy.

Question 31

# Fuzzy systems What do you use to build a FIS?

Answer 31

Data or knowledge/experience.

Question 32

# Fuzzy systems Can fuzzy systems be used for regression?

Answer 32

Yes.

Question 33

# Fuzzy systems Can fuzzy systems be used for clustering?

Answer 33

Yes.

Question 34

# Fuzzy systems How do you check how good a fuzzy system is?

Answer 34

Use error metrics like RMSE.

Question 35

# Fuzzy systems What is a neuro-fuzzy model?

Answer 35

A fuzzy model tuned using algorithms of NNs.

Question 36

# Fuzzy systems In a neuro-fuzzy system, what is tuned by the NN methods?

Answer 36

Locations and/or shapes of the membership functions.

Question 37

# Fuzzy systems What is ANFIS short for?

Answer 37

Adaptive Network-based Fuzzy Inference System

Question 38

# Fuzzy systems What is FCM short for?

Answer 38

Fuzzy Cognitive Maps

Question 39

# Fuzzy systems Who is behind FCM (Fuzzy Cognitive Maps)?

Answer 39

Kosko

Question 40

# Fuzzy systems What is Kosko known for?

Answer 40

FCM (Fuzzy Cognitive Maps)

Question 41

# Fuzzy systems What are FCMs?

Answer 41

FCMs are fuzzy graphs with possible feedback

Question 42

What's the difference between Mamdani-type and Sugeno-type FIS?

Answer 42

Mamdani has fuzzy outputs, and Sugeno uses a polynomial evaluation for outputs. Mamdani: If pressure is high, then volume is small Sugeno: If speed is medium, then resistance = 5*speed