Fuzzy Sets and Systems

Question 1

Fuzzy Logic Defenition

Answer 1

Multivariate logic that allows intermediate values between convetional (binary) evaluators like:
yes/no
true/false
black/white

Question 2

In Fuzzy systems, an attempt is made to apply a more ___ to the programming of computers

Answer 2

human-like way of thinking

Question 3

Example of The Sorites Paradox

Answer 3

How many clouds does it take to make a clear sky cloudy?

Question 4

Graduality/Fuzziness is the Conceptualization of the world based on concepts of ___, ___ and ___ (impreciseness)

Answer 4

similarity, gradualness and fuzziness

Question 5

Precision vs Relevance

Answer 5

Some time it is better to be relevant than to be precise. Example of the heavy weight dropping on top of someone

Question 6

Incompatibility Principle

Answer 6

As the complexity os systems increases, the hability to make relevant statements diminishes

Question 7

Fuzzy Sets

Answer 7

Sets with fuzzy (gradual) boundaries

Question 8

Integers larger than 3 are an example of Crisp or Fuzzy Sets?

Answer 8

Crisp

Question 9

Tall people are an example of Crisp or Fuzzy Sets?

Answer 9

Fuzzy

Question 10

What are Memberships Functions on Fuzzy Sets?

Answer 10

Functions that define if a point belongs to the fuzzy set

Question 11

Partition in Fuzzy Sets represents the division of the set into parts?

Answer 11

Yes

Question 12

Linguist Terms examples of Age

Answer 12

Young -> Old

Really Young -> Young but not too Young -> Not young not old ->…

Question 13

Core of Fuzzy Sets

Answer 13

Where the membership function is 1

Question 14

Support of Fuzzy Sets

Answer 14

Where the membership function is more than 0

Question 15

Singleton of Fuzzy Sets

Answer 15

Exception on membership function

Question 16

A Fuzzy Set is called normal if ___, otherwise it is called ___

Answer 16

its height is one

subnormal

Question 17

Set Theoric Operations:
1- Subset -> A contains B if ___
2- Complement -> Complement of A = X-A equivalent to ___
3- Union -> ___ of A and B membership functions
4- Intersection -> ___ of A and B membership functions

Answer 17

1- membership degree of A is less or equal to membership degree of B
2- membership degree of A = 1 - membership degree of B
3- Max
4- Min

Question 18

Mamdani Fuzzy Models are composed by a set of ___ rules where both ___ and ___ are fuzzy sets

Answer 18

if-then
antecedents
concequents

Question 19

Fuzzifier its an ___ between the ___ and the fuzzy system

Answer 19

interface

outside world

Question 20

A fuzzifier determines the match between ___ and the ___

Answer 20

a given input

linguistic terms

Question 21

Fuzzyfication is process of computing the ___ for crisp inputs or ___ for fuzzy inputs

Answer 21

membership

maximum membership

Question 22

Rulebase ___ the general relation between the ___ and the ___

Answer 22

encodes
inputs
outputs

Question 23

Inference Engine combines actual ___ with the ___ in the rule base to compute the ___ of the system

Answer 23

inputs
information encoded
fuzzy output

Question 24

The Degree of Fulfillment of the Inference Engine determines ___ the rule is ___

Answer 24

to what degree

valid

Question 25

The Output inference of the Inference Engine computes the ___ of ___ in the rule base, given the ___ of the rule base

Answer 25

output each fuzzy rule degree of fullfilment

Question 26

The Agreegation of the Inference Engine corresponds to calculating ___ from the relations of ___

Answer 26

the total relation | individual rules

Question 27

Defuzzifier computes a ___ that represents the ___

Answer 27

crisp number | output fuzzy set (defuzzification)

Question 28

Study Mandani Double Input

Answer 28

...

Question 29

Mamdani Fuzzy Models are composed by a set of ___ rules where ___ are fuzzy sets and ___ are ___

Answer 29

if-then antecedents consequents mathematical functions

Question 30

To develop a "Simple" Fuzzy Expert System: 1- Specify the ___ 2- Define ___ and respective 3- Determine ___ 4- Elicit and construct ___ 5- Encode the fuzz sets, fuzzy rules and procedures in order to perform ___ 6- ___ and ___ the system

Answer 30

``` 1- problem 2- linguistic variables / linguistic terms 3- Fuzzy Sets 4- Fuzzy Rules 5- fuzzy inference 6- Evaluate and Tune ```

Question 31

Some advantages of Fuzzy Systems are: 1- Considerable ___ for little ___ 2- ___ Fuzzy rules and fuzzy systems are (usually) ___ by humans

Answer 31

1- skill / investment | 2- Interpretability / understandable

Question 32

Some motives to avoid using fuzzy rule based systems are: 1- Humans do not ___ the system 2- Different experts ___ 3- Knowledge cannot be expressed with ___

Answer 32

1- understand 2- disagree 3- verbal rules

Question 33

We can increase the accuracy of a mapping by ___ the number of rules in the rule base 1- Best results are obtained when the number of linguistic terms in the __ and the ___ are increased 2- However, using too many linguistic terms ___ of fuzzy systems and leads to

Answer 33

``` increasing input /output diminishes the transparency combinatorial rule explosion ```

Question 34

Fuzzy systems’ rulebases become ___ to | implement with the increase of the number of inputs

Answer 34

exponentially harder