### User-Friendly Fuzzy FCA

```User-Friendly Fuzzy FCA
ICFCA 2013
Dresden, Germany
Juraj Macko, Palacky University, Olomouc, Czech Republic
User-Friendly Fuzzy FCA
User-Friendly
Fuzzy FCA
is oxymoron.
Isn’t it? 
FCA has strong mathematical foundations.
FCA has a very clear meaning for users.
Fuzzy FCA has strong mathematical foundations.
Fuzzy FCA does NOT have a clear meaning for users.
User-Friendly Fuzzy FCA
Fuzzy set
Residuated
lattice
Lukasiewicz
Fuzzy concept lattice
User R.I.P.!
Godel
Fuzzy relation
User-Friendly Fuzzy FCA
Half - red
circles
Measuring
cup
Object
Liquid color
Attribute
User-Friendly Fuzzy FCA
C
yan
Printer 1
Printer 2
M
agenta
Y
ellow
K
ey (black)
User-Friendly Fuzzy FCA
Universum X = All objects = {x1, x2, x3, x4,}
x1
x2
x3
x4
x1
x2
x3
x4
x1
x2
x3
x4
Set A = Objects which we care about = {x1, x4,}
FCA: What you share, iF you Care About.
Set A = for each object from X we specify
either “We care about”
or “We do not care about”
We care about = We care about in degree 1
We do not care about = We care about in degree 0
Fuzzy Set A(x) = for each object from X we specify
How much we care about
(in which degree)
User-Friendly Fuzzy FCA
Part of the
object,
which we
Actual
amount of
RED in object
User-Friendly Fuzzy FCA
<=
Is it TRUE, that the part,
which we care about is
RED?
Yes, it is TRUE.
truth degree = 1
User-Friendly Fuzzy FCA
>=
Is it TRUE, that the part,
which we care about is
RED?
No, it is not
TRUE.
truth degree = 0
User-Friendly Fuzzy FCA
>
It is TRUE
in truth degree…
How much is TRUE, that
the part, which we care
?
?
?
?
?
User-Friendly Fuzzy FCA
>
How much is TRUE, that
the part, which we care
It is TRUE
in truth degree
2/5.
Material truth
=
actual amount of
color.
User-Friendly Fuzzy FCA
>
It is TRUE
It is TRUE
in truth degree
in truth degree 1.
1 - 3/5
1/5 = 3/5
2/5
4/5
2/5
How much is TRUE, that
the part, which we care
X
X
X
X
X
X
Similarity truth
=
How similar it is
comparing to
TRUE
(truth degree 1)
Error-like truth
=
How much is left to
be TRUE
(truth degree 1)
User-Friendly Fuzzy FCA
>
How much is TRUE, that
the part, which we care
It is TRUE
in truth degree
2/3.
Proportional
=
what you see
/
what you care
User-Friendly Fuzzy FCA
Mr.
Godel
Mr.
Lukasiewicz
Mr.
Product
User-Friendly Fuzzy FCA
1
Mr.
Godel
Mr.
Lukasiewicz
Mr.
Product
User-Friendly Fuzzy FCA
0
Fuzzy
negation
Mr.
Godel
Mr.
Lukasiewicz
Mr.
Product
I(x,y)
A(x)
How much we
object
How much is TRUE, that
the part, which we care
Sharing
=
Taking minimal
truth degree
B(y)
maximality
A(x)
Sharing
=
Taking minimal
truth degree
Has an object the
amount of RED, which
Has an object the
required amount of
RED?
I(x,y)
B(y)
How much we
attribute.
User-Friendly Fuzzy FCA
Hedge – thruth stressing
Original statement:
The teeth are white.
Stronger statement:
The teeth are snow-white.
The teeth are very white.
It is very true, that the teeth are white.
1. The original statement:
We care about the object.
2. The statement with the identity hedge (a*=a):
We normally care about the object.
3. The statement with the globalization hedge (a*=0, a<1):
We fully care about the object.
User-Friendly Fuzzy FCA
Scaling
Godel
Scale
Lukasiewicz
Scale
Godel
Scale
User-Friendly Fuzzy FCA
Lukasiewicz
Scale
Godel
Scale
Godel
Scale
Lukasiewicz
Scale
Lukasiewicz
Scale
User-Friendly Fuzzy FCA
Scaled fuzzy context
Lukasiewicz
Data source:
Belohlavek R., FRS
User-Friendly Fuzzy FCA
Any real application?
Fuzzy FCA with measures
FCA
with measures
OLAP Cube
DB: Group by
Fuzzy OLAP Cube
DB: Fuzzy group by
User-Friendly Fuzzy FCA
Fuzzy OLAP
application?
Data source:
Belohlavek R., FRS
NASA
User-Friendly Fuzzy FCA
User-Friendly
Fuzzy FCA
Oxymoron?
User-Friendly Fuzzy FCA
C
Printer 1
Printer 2
M
Y
K
```