Similarity issues in attribute implications from data with fuzzy attributes

We study similarity in formal concept analysis of data tables with fuzzy attributes. We focus on similarity related to attribute implications, i.e. rules A rArr B describing dependencies "each object which has all attributes from A has also all attributes from B". We present several formulas for estimation of similarity of outputs in terms of similarity of inputs. The results answer some natural questions such as how much do truth degrees of A1 rArr B and A2 rArr B differ in terms of similarity of A1 to A2?

[1]  Radim Bělohlávek,et al.  Fuzzy attribute logic : syntactic entailment and completeness Radim Bělohlávek Vilém Vychodil , 2005 .

[2]  Petr Hájek,et al.  On very true , 2001, Fuzzy Sets Syst..

[3]  L. Beran,et al.  [Formal concept analysis]. , 1996, Casopis lekaru ceskych.

[4]  J. Goguen.  L-fuzzy sets , 1967 .

[5]  Vilém Vychodil,et al.  Estimations of Similarity in Formal Concept Analysis of Data with Graded Attributes , 2006, Advances in Web Intelligence and Data Mining.

[6]  R. Belohlávek.  Fuzzy Relational Systems: Foundations and Principles , 2002 .

[7]  Vilém Vychodil,et al.  Axiomatizations of Fuzzy Attribute Logic , 2005, IICAI.

[8]  Vilém Vychodil,et al.  Axiomatization of Fuzzy Attribute Logic over Complete Residuated Lattices , 2006, JCIS.

[9]  Radim Belohlávek,et al.  Similarity relations in concept lattices , 2000, J. Log. Comput..

[10]  Bernhard Ganter,et al.  Formal Concept Analysis: Mathematical Foundations , 1998 .

[11]  R. Belohlávek,et al.  GALOIS CONNECTIONS WITH HEDGES ∗ , 2005 .

[12]  Lotfi A. Zadeh,et al.  Similarity relations and fuzzy orderings , 1971, Inf. Sci..

[13]  Vilém Vychodil,et al.  Reducing the Size of Fuzzy Concept Lattices by Hedges , 2005, The 14th IEEE International Conference on Fuzzy Systems, 2005. FUZZ '05..

[14]  Radim Belohlávek,et al.  Fast factorization by similarity in formal concept analysis of data with fuzzy attributes , 2007, J. Comput. Syst. Sci..

[15]  Radim Bělohlávek,et al.  Fuzzy Relational Systems: Foundations and Principles , 2002 .

[16]  R. Belohlávek,et al.  FUZZY ATTRIBUTE LOGIC : ATTRIBUTE IMPLICATIONS , THEIR VALIDITY , ENTAILMENT , AND NON-REDUNDANT BASIS ∗ , 2005 .

[17]  Vilém Vychodil,et al.  Functional Dependencies of Data Tables Over Domains with Similarity Relations , 2005, IICAI.

[18]  Claudio Carpineto,et al.  Concept data analysis - theory and applications , 2004 .

[19]  Radim B̌elohĺavek,et al.  Implications from data with fuzzy attributes , 2004 .

[20]  Radim Belohlávek,et al.  Concept lattices and order in fuzzy logic , 2004, Ann. Pure Appl. Log..

[21]  David Maier,et al.  The Theory of Relational Databases , 1983 .

[22]  Satoko Titani,et al.  Globalization of intui tionistic set theory , 1987, Ann. Pure Appl. Log..

[23]  Vilém Vychodil,et al.  Attribute Implications in a Fuzzy Setting , 2006, ICFCA.

[24]  Ramón Fuentes-González,et al.  The study of the L-fuzzy concept lattice , 1994 .

[25]  Vilém Vychodil,et al.  Implications from data with fuzzy attributes vs. scaled binary attributes , 2005, The 14th IEEE International Conference on Fuzzy Systems, 2005. FUZZ '05..

[26]  Vincent Duquenne,et al.  Familles minimales d'implications informatives résultant d'un tableau de données binaires , 1986 .

[27]  Petr Hájek,et al.  Metamathematics of Fuzzy Logic , 1998, Trends in Logic.