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

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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.

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

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

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

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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.

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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.

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

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

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

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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.

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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

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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.

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

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

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

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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

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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

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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.

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User-Friendly Fuzzy FCA Godel Scale Lukasiewicz Scale Scaling

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

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

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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

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

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User-Friendly Fuzzy FCA Oxymoron?

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CMYK Printer 1 Printer 2 User-Friendly Fuzzy FCA

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