Attribute dependencies for data with grades II*,†

Abstract In the second part of this two-part paper, we present results and algorithms regarding redundancy and complete non-redundant sets of dependencies, examine a relationship to and a possible reductionist interface to classical dependencies and a relationship to functional dependencies over domains with similarity relations. We also outline future research topics.

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

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

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

[4]  Vilém Vychodil,et al.  Reducing attribute implications from data tables with fuzzy attributes to tables with binary attributes , 2005 .

[5]  Bernhard Ganter,et al.  Formal Concept Analysis , 2013 .

[6]  Brian A. Davey,et al.  An Introduction to Lattices and Order , 1989 .

[7]  W. W. Armstrong,et al.  Dependency Structures of Data Base Relationships , 1974, IFIP Congress.

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

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

[10]  Vilém Vychodil,et al.  Fuzzy Attribute Implications: Computing Non-redundant Bases Using Maximal Independent Sets , 2005, Australian Conference on Artificial Intelligence.

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

[12]  A. J. M. van Gasteren,et al.  An Introduction to Three Algorithms for Sorting in Situ , 1982, Inf. Process. Lett..

[13]  F. E..  A Relational Model of Data Large Shared Data Banks , 2000 .

[14]  Sergei O. Kuznetsov,et al.  Some decision and counting problems of the Duquenne-Guigues basis of implications , 2008, Discret. Appl. Math..

[15]  S. Gottwald.  A Treatise on Many-Valued Logics , 2001 .

[16]  Philip A. Bernstein,et al.  Decomposition of a Data Base and the Theory of Boolean Switching Functions , 1973, IBM J. Res. Dev..

[17]  Vilem Vychodil,et al.  Properties of models of fuzzy attribute implications , 2006 .

[18]  Vilém Vychodil,et al.  Fuzzy Closure Operators with Truth Stressers , 2005, Log. J. IGPL.

[19]  Daniel T. Larose,et al.  Discovering Knowledge in Data: An Introduction to Data Mining , 2005 .

[20]  Ronald Fagin,et al.  Combining Fuzzy Information from Multiple Systems , 1999, J. Comput. Syst. Sci..

[21]  A. D. Forbes,et al.  On independent sets , 2005 .

[22]  Peter Jipsen,et al.  Residuated lattices: An algebraic glimpse at sub-structural logics , 2007 .

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

[24]  Kristin P. Bennett,et al.  Support vector machines: hype or hallelujah? , 2000, SKDD.

[25]  Giangiacomo Gerla,et al.  Fuzzy Logic: Mathematical Tools for Approximate Reasoning , 2001 .

[26]  T. Havránek,et al.  Mechanizing Hypothesis Formation: Mathematical Foundations for a General Theory , 1978 .

[27]  Jan Pavelka,et al.  On Fuzzy Logic I Many-valued rules of inference , 1979, Math. Log. Q..

[28]  Vilém Vychodil,et al.  Formal concept analysis and linguistic hedges , 2012, Int. J. Gen. Syst..

[29]  Arun K. Majumdar,et al.  Fuzzy Functional Dependencies and Lossless Join Decomposition of Fuzzy Relational Database Systems , 1988, ACM Trans. Database Syst..

[30]  Gregory S. Richardson,et al.  The structure of fuzzy preferences: Social choice implications , 1998 .

[31]  Lotfi A. Zadeh,et al.  Is there a need for fuzzy logic? , 2008, NAFIPS 2008 - 2008 Annual Meeting of the North American Fuzzy Information Processing Society.

[32]  Mihalis Yannakakis,et al.  On Generating All Maximal Independent Sets , 1988, Inf. Process. Lett..

[33]  G. Mayor,et al.  Triangular norms on discrete settings , 2005 .

[34]  Tomasz Imielinski,et al.  Mining association rules between sets of items in large databases , 1993, SIGMOD Conference.

[35]  Petr Hájek,et al.  The GUHA method and its meaning for data mining , 2010, J. Comput. Syst. Sci..

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

[37]  Petr Hájek,et al.  What is mathematical fuzzy logic , 2006, Fuzzy Sets Syst..

[38]  Lotfi A. Zadeh,et al.  Fuzzy logic, neural networks, and soft computing , 1993, CACM.

[39]  C.J.H. Mann,et al.  Fuzzy Relational Systems: Foundations and Principles , 2003 .

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

[41]  Vilém Vychodil,et al.  Attribute Dependencies for Data with Grades , 2014, ArXiv.

[42]  Vilém Vychodil,et al.  A logic of graded attributes , 2015, Arch. Math. Log..

[43]  Ulrich Güntzer,et al.  Algorithms for association rule mining — a general survey and comparison , 2000, SKDD.

[44]  Ronald Fagin,et al.  Combining fuzzy information: an overview , 2002, SGMD.

[45]  Radim Belohlávek,et al.  Fuzzy Galois Connections , 1999, Math. Log. Q..

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

[47]  Ronald Fagin,et al.  Functional Dependencies in a Relational Data Base and Propositional Logic , 1977, IBM J. Res. Dev..

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

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

[50]  Vilém Vychodil,et al.  Codd's Relational Model from the Point of View of Fuzzy Logic , 2011, J. Log. Comput..

[51]  Siegfried Gottwald,et al.  Mathematical Fuzzy Logics , 2008, Bulletin of Symbolic Logic.