Fuzzy Sets and Systems Flashcards
Fuzzy Logic Defenition
Multivariate logic that allows intermediate values between convetional (binary) evaluators like:
yes/no
true/false
black/white
In Fuzzy systems, an attempt is made to apply a more ___ to the programming of computers
human-like way of thinking
Example of The Sorites Paradox
How many clouds does it take to make a clear sky cloudy?
Graduality/Fuzziness is the Conceptualization of the world based on concepts of ___, ___ and ___ (impreciseness)
similarity, gradualness and fuzziness
Precision vs Relevance
Some time it is better to be relevant than to be precise. Example of the heavy weight dropping on top of someone
Incompatibility Principle
As the complexity os systems increases, the hability to make relevant statements diminishes
Fuzzy Sets
Sets with fuzzy (gradual) boundaries
Integers larger than 3 are an example of Crisp or Fuzzy Sets?
Crisp
Tall people are an example of Crisp or Fuzzy Sets?
Fuzzy
What are Memberships Functions on Fuzzy Sets?
Functions that define if a point belongs to the fuzzy set
Partition in Fuzzy Sets represents the division of the set into parts?
Yes
Linguist Terms examples of Age
Young -> Old
Really Young -> Young but not too Young -> Not young not old ->…
Core of Fuzzy Sets
Where the membership function is 1
Support of Fuzzy Sets
Where the membership function is more than 0
Singleton of Fuzzy Sets
Exception on membership function
A Fuzzy Set is called normal if ___, otherwise it is called ___
its height is one
subnormal
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
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
Mamdani Fuzzy Models are composed by a set of ___ rules where both ___ and ___ are fuzzy sets
if-then
antecedents
concequents
Fuzzifier its an ___ between the ___ and the fuzzy system
interface
outside world
A fuzzifier determines the match between ___ and the ___
a given input
linguistic terms
Fuzzyfication is process of computing the ___ for crisp inputs or ___ for fuzzy inputs
membership
maximum membership
Rulebase ___ the general relation between the ___ and the ___
encodes
inputs
outputs
Inference Engine combines actual ___ with the ___ in the rule base to compute the ___ of the system
inputs
information encoded
fuzzy output
The Degree of Fulfillment of the Inference Engine determines ___ the rule is ___
to what degree
valid
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
The Agreegation of the Inference Engine corresponds to calculating ___ from the relations of ___
the total relation
individual rules
Defuzzifier computes a ___ that represents the ___
crisp number
output fuzzy set (defuzzification)
Study Mandani Double Input
…
Mamdani Fuzzy Models are composed by a set of ___ rules where ___ are fuzzy sets and ___ are ___
if-then
antecedents
consequents
mathematical functions
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
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
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
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
Fuzzy systems’ rulebases become ___ to
implement with the increase of the number of inputs
exponentially harder
