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User-Friendly Fuzzy FCA ICFCA 2013 Dresden, Germany Juraj Macko, Palacky University, Olomouc, Czech Republic.

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Presentation on theme: "User-Friendly Fuzzy FCA ICFCA 2013 Dresden, Germany Juraj Macko, Palacky University, Olomouc, Czech Republic."— Presentation transcript:

1 User-Friendly Fuzzy FCA ICFCA 2013 Dresden, Germany Juraj Macko, Palacky University, Olomouc, Czech Republic

2 User-Friendly Fuzzy FCA is oxymoron. Isnt it? User-Friendly Fuzzy FCA 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.

3 Residuated lattice Fuzzy set Fuzzy relation Arrow operators User-Friendly Fuzzy FCA Fuzzy concept lattice Godel Lukasiewicz User R.I.P.!

4 Half - red circles Measuring cup Object Liquid color Attribute User-Friendly Fuzzy FCA

5 C yan M agenta Y ellow K ey (black) Printer 1 Printer 2 User-Friendly Fuzzy FCA

6 x1x1 x2x2 x3x3 x4x4 Universum X = All objects = {x 1, x 2, x 3, x 4, } Set A = Objects which we care about = {x 1, x 4, } x1x1 x2x2 x3x3 x4x4 x1x1 x2x2 x3x3 x4x4 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) FCA: What you share, iF you Care About.

7 Part of the object, which we care about. Part of the object, which we care about. Actual amount of RED in object User-Friendly Fuzzy FCA Part of the object, which we care about.

8 = Is it TRUE, that the part, which we care about is RED? < User-Friendly Fuzzy FCA Yes, it is TRUE. truth degree = 1

9 = Is it TRUE, that the part, which we care about is RED? > User-Friendly Fuzzy FCA No, it is not TRUE. truth degree = 0

10 It is TRUE in truth degree… How much is TRUE, that the part, which we care about is RED? > ? ? ? ? ? User-Friendly Fuzzy FCA

11 How much is TRUE, that the part, which we care about is RED? Material truth = actual amount of color. User-Friendly Fuzzy FCA > It is TRUE in truth degree 2/5.

12 X X X X X X How much is TRUE, that the part, which we care about is RED? It is TRUE in truth degree 1. It is TRUE in truth degree 1 - 1/5 = 4/5 It is TRUE in truth degree 1 - 2/5 = 3/5 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 > It is TRUE in truth degree 1 - 3/5 = 2/5

13 How much is TRUE, that the part, which we care about is RED? Proportional = what you see / what you care about User-Friendly Fuzzy FCA > It is TRUE in truth degree 2/3.

14 Mr. Godel Mr. Lukasiewicz Mr. Product User-Friendly Fuzzy FCA

15 Mr. Godel Mr. Lukasiewicz Mr. Product 1 User-Friendly Fuzzy FCA

16 Mr. Godel Mr. Lukasiewicz Mr. Product 0 Fuzzy negation User-Friendly Fuzzy FCA

17 A(x) B(y) I(x,y) How much we care about the object How much is TRUE, that the part, which we care about is RED? Sharing = Taking minimal truth degree

18 B(y) A(x) I(x,y) How much we care about the attribute. Has an object the amount of RED, which we care about? Has an object the required amount of RED? Sharing = Taking minimal truth degree maximality

19 User-Friendly Fuzzy FCA 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. Hedge – thruth stressing 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.

20 User-Friendly Fuzzy FCA Godel Scale Lukasiewicz Scale Scaling

21 User-Friendly Fuzzy FCA Godel Scale Lukasiewicz Scale Godel Scale Lukasiewicz Scale Godel Scale Lukasiewicz Scale

22 User-Friendly Fuzzy FCA Data source: Belohlavek R., FRS Scaled fuzzy context Lukasiewicz

23 FCA with measures User-Friendly Fuzzy FCA Any real application? OLAP Cube DB: Group by Fuzzy OLAP Cube DB: Fuzzy group by Fuzzy FCA with measures

24 User-Friendly Fuzzy FCA Fuzzy OLAP application? Data source: Belohlavek R., FRS NASA

25 User-Friendly Fuzzy FCA Oxymoron?

26 CMYK Printer 1 Printer 2 User-Friendly Fuzzy FCA


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