Yapay Zeka`ya giris

Yapay Zeka’ya giris
Yapay sinir aglari ve bulanik mantik
Uzay CETIN
Université Pierre Marie Curie (Paris VI),
Master 2 Recherche, Agents Intelligents, Apprentissage et Décision (AIAD)
November 18, 2008
Uzay CETIN ()
Yapay Zeka’ya giris
November 18, 2008
1 / 44
soft computing
Icindekiler
1
soft computing
2
fuzzy logic
3
Neurofuzzy Modelling
YSA
genel olarak yapay sinir aglari
4
Bulanik Mantik
bulanik. akil yurutme
bulanik. akil yurutme
Uzay CETIN ()
Yapay Zeka’ya giris
November 18, 2008
2 / 44
soft computing
Soft computing, parallels the remarkable ability of human mind to reason
and learn in an environment of uncertainty and imprecision.
Figure: A neural character recogniser and a knowladge base cooperation
Uzay CETIN ()
Yapay Zeka’ya giris
November 18, 2008
3 / 44
soft computing
Figure: A fuzzy inference system
Uzay CETIN ()
Yapay Zeka’ya giris
November 18, 2008
4 / 44
soft computing
Soft computing is a discipline situated at the combination of several
relatively new and distinct mathematical techniques:
fuzzy logic
neural networks
probabilistic reasoning (PR) which include genetic algorithms, chaos
theory, belief nets and learning theory.
Uzay CETIN ()
Yapay Zeka’ya giris
November 18, 2008
5 / 44
fuzzy logic
Icindekiler
1
soft computing
2
fuzzy logic
3
Neurofuzzy Modelling
YSA
genel olarak yapay sinir aglari
4
Bulanik Mantik
bulanik. akil yurutme
bulanik. akil yurutme
Uzay CETIN ()
Yapay Zeka’ya giris
November 18, 2008
6 / 44
fuzzy logic
It is based on the idea that sets are not crisp but some are fuzzy, and these
can be modeled in linguistic human terms such as large, small and
medium.
what is the advantage?
This results in fewer rules and lower computer resources.
Uzay CETIN ()
Yapay Zeka’ya giris
November 18, 2008
7 / 44
fuzzy logic
It is based on the idea that sets are not crisp but some are fuzzy, and these
can be modeled in linguistic human terms such as large, small and
medium.
what is the advantage?
This results in fewer rules and lower computer resources.
Uzay CETIN ()
Yapay Zeka’ya giris
November 18, 2008
7 / 44
fuzzy logic
Modeling of the human operators behavior.
In fuzzy systems, rules can be formulated that use these linguistic
expressions and apply them to the human behavioral problem.
Fuzzy inference systems are an extension of classical AI techniques that
incorporate human knowledge and perform uncertain reasoning.
Uzay CETIN ()
Yapay Zeka’ya giris
November 18, 2008
8 / 44
fuzzy logic
In the supervised learning process input-output pairs of a process are
used for training.
In some cases genetic or evolutionary algorithms which are
derivative-free optimization techniques
Uzay CETIN ()
Yapay Zeka’ya giris
November 18, 2008
9 / 44
Neurofuzzy Modelling
Icindekiler
1
soft computing
2
fuzzy logic
3
Neurofuzzy Modelling
YSA
genel olarak yapay sinir aglari
4
Bulanik Mantik
bulanik. akil yurutme
bulanik. akil yurutme
Uzay CETIN ()
Yapay Zeka’ya giris
November 18, 2008
10 / 44
Neurofuzzy Modelling
Why combination
A neural network
A neural network can approximate a function, with adjusted weights, but
it is impossible to interpret the result in terms of natural language.
A fuzzy system
a fuzzy rule base consists of readable if-then statements that are almost
natural language, but it cannot learn the rules itself.
So combination
Uzay CETIN ()
Yapay Zeka’ya giris
November 18, 2008
11 / 44
Neurofuzzy Modelling
Extracting rules from data
The goal is to reduce the complexity in a problem, or to reduce the
amount of data associated with a problem. The inference mechanism
If f (e1 is A1 , e2 is A2 , . . . , ek is Ak ) then y = g (e1 , e2 , . . . , ek )
(1)
Here f is a logical function that connects the sentences forming the
condition, y is the output, and g is a function of the inputs ei .
Uzay CETIN ()
Yapay Zeka’ya giris
November 18, 2008
12 / 44
Neurofuzzy Modelling
Feature determination
In general, data analysis (Zimmermann, 1993) concerns objects which are
described by features.
The features form axes of an abstract feature space in which each object is
represented by a point. For instance, in the four-dimensional coordinate
system spanned by the axes top speed, colour, air resistance, and weight.
So a vehicle V1 can be represented by the point
(x1 , x2 , x3 , x4) = (220, red, 0.30, 1300).
Uzay CETIN ()
Yapay Zeka’ya giris
November 18, 2008
13 / 44
Neurofuzzy Modelling
The latter option is necessary in case a large number of features
needs to be reduced to a smaller number of features.
Objects are fuzzy when one or more features are described in fuzzy
terms.
An example is a vehicle with a very fast car engine, rather than top
speed equal to some crisp number.
Uzay CETIN ()
Yapay Zeka’ya giris
November 18, 2008
14 / 44
Neurofuzzy Modelling
Figure: bulanik iliski
Uzay CETIN ()
Yapay Zeka’ya giris
November 18, 2008
15 / 44
Neurofuzzy Modelling
Figure: bulanik iliski
Uzay CETIN ()
Yapay Zeka’ya giris
November 18, 2008
16 / 44
Neurofuzzy Modelling
(two clusters)
Each point belongs to one or the other class, so the clusters are crisp.
Uzay CETIN ()
Yapay Zeka’ya giris
November 18, 2008
17 / 44
Neurofuzzy Modelling
Bulanik kume ornekleri
IF height is tall
THEN weight is heavy.
Figure: bulanik iliski
Uzay CETIN ()
Yapay Zeka’ya giris
November 18, 2008
18 / 44
Neurofuzzy Modelling
Bulanik kume ornekleri
kucukler ve buyukler, iki tane bulanik kume olsun
U = V = {1, 2, 3, 4}
kucukler = 1.0/1 + 0.6/2 + 0.1/3 + 0.0/4
buyukler = 0.0/1 + 0.1/2 + 0.6/3 + 1.0/4
5’e yakin olan sayilar, S5 ile gosterilsin,
S5 = 0.0/2 + 0.1/3 + 0.6/4 + 1.0/5 + 0.6/6 + 0.1/7 + 0.0/8
burdaki toplama isareti cebirsel toplama isareti degil sadece toplu
gosterim amacini tasiyor.
Uzay CETIN ()
Yapay Zeka’ya giris
November 18, 2008
19 / 44
Neurofuzzy Modelling
bulanik. akil yurutme
Icindekiler
1
soft computing
2
fuzzy logic
3
Neurofuzzy Modelling
YSA
genel olarak yapay sinir aglari
4
Bulanik Mantik
bulanik. akil yurutme
bulanik. akil yurutme
Uzay CETIN ()
Yapay Zeka’ya giris
November 18, 2008
20 / 44
Neurofuzzy Modelling
bulanik. akil yurutme
Kural yapisi
IF (x1 is A1 ) AND (y1 is B1 ) THEN (z1 is C1 )
µA∪B (x) = max[µA (x), µB (x)]
µA∩B (x) = min[µA (x), µB (x)]
Figure: bulaniklastirma islemi
Uzay CETIN ()
Yapay Zeka’ya giris
November 18, 2008
21 / 44
Neurofuzzy Modelling
bulanik. akil yurutme
Avantaji nedir?
Cok sayidaki gercel degerler, birkac tane bulanik degiskenle ifade
edilebiliyor.
Az sayidaki kuralla akil yurutme yapilabiliyor. kompakt!!!
Figure: bulaniklastirma islemi
Uzay CETIN ()
Yapay Zeka’ya giris
November 18, 2008
22 / 44
Neurofuzzy Modelling
bulanik. akil yurutme
Icindekiler
1
soft computing
2
fuzzy logic
3
Neurofuzzy Modelling
YSA
genel olarak yapay sinir aglari
4
Bulanik Mantik
bulanik. akil yurutme
bulanik. akil yurutme
Uzay CETIN ()
Yapay Zeka’ya giris
November 18, 2008
23 / 44
Neurofuzzy Modelling
bulanik. akil yurutme
Kural yapisi
Figure: bulanik cikarim
Uzay CETIN ()
Yapay Zeka’ya giris
November 18, 2008
24 / 44
Neurofuzzy Modelling
bulanik. akil yurutme
Kural yapisi
burda kurallarin ciktilarinin tumunu ayni potada eritiyoruz.
Figure: bulanik birlestirme
simdi geriye kalan islem durulastirma. bunun icin de cesitli yontemler var.
onlardan biri agirlik noktasi bulma yontemi. bu ortaya cikan sekli iki esit
agirliga X eksenine dik ir cizgi ile ayirir.
Uzay CETIN ()
Yapay Zeka’ya giris
November 18, 2008
25 / 44
Neurofuzzy Modelling
bulanik. akil yurutme
Sugeno-style
Figure: bulanik birlestirme
Uzay CETIN ()
Yapay Zeka’ya giris
November 18, 2008
26 / 44
Neurofuzzy Modelling
bulanik. akil yurutme
Sugeno-style aggregation
Figure: bulanik birlestirme
Uzay CETIN ()
Yapay Zeka’ya giris
November 18, 2008
27 / 44
Neurofuzzy Modelling
bulanik. akil yurutme
Sugeno-style aggregation
Figure: bulanik birlestirme
Uzay CETIN ()
Yapay Zeka’ya giris
November 18, 2008
28 / 44
Ozet
son
Tesekkurler...
bir sonraki derste, Bulanik mantik ve yapay sinir aglarini uygulamalarina
giricez. takip edecegimiz kitap : C++ Neural Networks and Fuzzy Logic Valluru B. Rao
Uzay CETIN ()
Yapay Zeka’ya giris
November 18, 2008
29 / 44
Appendix
Referanslar
Referanslar I
Bernhard Nebel, Gnther Grz
Yapay Zeka, Inkilap Kitabevi.
wikipedia
http://en.wikipedia.org/wiki/Monty Hall problem
Uzay CETIN ()
Yapay Zeka’ya giris
November 18, 2008
30 / 44