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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.

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User-Friendly Fuzzy FCA

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

  2. 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.

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

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

  5. User-Friendly Fuzzy FCA Cyan Magenta Yellow Key (black) Printer 1 Printer 2

  6. User-Friendly Fuzzy FCA x1 x2 x3 x4 Universum X = All objects = {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 x1 x2 x3 x4 Fuzzy Set A(x) = for each object from X we specify How much we care about (in which degree) x1 x2 x3 x4

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

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

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

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

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

  12. User-Friendly Fuzzy FCA > 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 It is TRUE in truth degree 1 - 3/5 = 2/5 How much is TRUE, that the part, which we care about is RED? Similarity truth = How similar it is comparing to TRUE (truth degree 1) X X X X Error-like truth = How much is left to be TRUE (truth degree 1) X X

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

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

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

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

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

  18. I(x,y) maximality A(x) B(y) Sharing = Taking minimal truth degree 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?

  19. User-Friendly Fuzzy FCA Hedge – thruth stressing Stronger statement: The teeth are snow-white. The teeth are very white. Itisverytrue, that the teeth are white. Original statement: Theteeth are white. 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 Scaling Lukasiewicz Scale Godel Scale

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

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

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

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

  25. User-Friendly Fuzzy FCA User-Friendly Fuzzy FCA Oxymoron?

  26. User-Friendly Fuzzy FCA C M Y K Printer 1 Printer 2

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