Fuzzy Sets and Systems Flashcards

1
Q

Fuzzy Logic Defenition

A

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

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2
Q

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

A

human-like way of thinking

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3
Q

Example of The Sorites Paradox

A

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

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4
Q

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

A

similarity, gradualness and fuzziness

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5
Q

Precision vs Relevance

A

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

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6
Q

Incompatibility Principle

A

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

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7
Q

Fuzzy Sets

A

Sets with fuzzy (gradual) boundaries

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8
Q

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

A

Crisp

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9
Q

Tall people are an example of Crisp or Fuzzy Sets?

A

Fuzzy

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10
Q

What are Memberships Functions on Fuzzy Sets?

A

Functions that define if a point belongs to the fuzzy set

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11
Q

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

A

Yes

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12
Q

Linguist Terms examples of Age

A

Young -> Old

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

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13
Q

Core of Fuzzy Sets

A

Where the membership function is 1

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14
Q

Support of Fuzzy Sets

A

Where the membership function is more than 0

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15
Q

Singleton of Fuzzy Sets

A

Exception on membership function

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16
Q

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

A

its height is one

subnormal

17
Q

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

A

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

18
Q

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

A

if-then
antecedents
concequents

19
Q

Fuzzifier its an ___ between the ___ and the fuzzy system

A

interface

outside world

20
Q

A fuzzifier determines the match between ___ and the ___

A

a given input

linguistic terms

21
Q

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

A

membership

maximum membership

22
Q

Rulebase ___ the general relation between the ___ and the ___

A

encodes
inputs
outputs

23
Q

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

A

inputs
information encoded
fuzzy output

24
Q

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

A

to what degree

valid

25
The Output inference of the Inference Engine computes the ___ of ___ in the rule base, given the ___ of the rule base
output each fuzzy rule degree of fullfilment
26
The Agreegation of the Inference Engine corresponds to calculating ___ from the relations of ___
the total relation | individual rules
27
Defuzzifier computes a ___ that represents the ___
crisp number | output fuzzy set (defuzzification)
28
Study Mandani Double Input
...
29
Mamdani Fuzzy Models are composed by a set of ___ rules where ___ are fuzzy sets and ___ are ___
if-then antecedents consequents mathematical functions
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
``` 1- problem 2- linguistic variables / linguistic terms 3- Fuzzy Sets 4- Fuzzy Rules 5- fuzzy inference 6- Evaluate and Tune ```
31
Some advantages of Fuzzy Systems are: 1- Considerable ___ for little ___ 2- ___ Fuzzy rules and fuzzy systems are (usually) ___ by humans
1- skill / investment | 2- Interpretability / understandable
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 ___
1- understand 2- disagree 3- verbal rules
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
``` increasing input /output diminishes the transparency combinatorial rule explosion ```
34
Fuzzy systems’ rulebases become ___ to | implement with the increase of the number of inputs
exponentially harder