Reducing the Size of If-Then Rules Generated from Data Tables with Graded Attributes

Presented is a method for reducing the size of if-then rules generated from data tables with graded attributes. Data tables with graded attributes represent data structures describing graded properties of objects. We show a method for generating of particular reduced and minimal set of if-then rules which describe all dependencies which are valid in a given data table with graded attributes. We present theoretical insight, algorithms, and illustrative examples.

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

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

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

[4]  Vilém Vychodil,et al.  Data Tables with Similarity Relations: Functional Dependencies, Complete Rules and Non-redundant Bases , 2006, DASFAA.

[5]  Dimitar P. Filev,et al.  Fuzzy SETS AND FUZZY LOGIC , 1996 .

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

[7]  J. A. Goguen,et al.  The logic of inexact concepts , 1969, Synthese.

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

[9]  George J. Klir,et al.  Fuzzy sets and fuzzy logic - theory and applications , 1995 .

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

[11]  Petr Hájek.  On very true , 2001, Fuzzy Sets Syst..

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

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

[14]  Chengqi Zhang,et al.  Association Rule Mining , 2002, Lecture Notes in Computer Science.

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

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

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

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

[19]  Shichao Zhang,et al.  Association Rule Mining: Models and Algorithms , 2002 .

[20]  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..

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