An efficient method to factorize fuzzy attribute-oriented concept lattices

Abstract Factorization by similarity is a mathematical technique used in formal concept analysis with fuzzy attributes for reducing the complexity of different types of fuzzy concept lattices. In this paper we find the structure of the factor lattice of a fuzzy attribute-oriented concept lattice, namely the intervals representing the blocks of this lattice. We provide a procedure for generating the infimum and the supremum concepts of these intervals as fixpoints of a fuzzy closure operator. This theoretical result allows to develop a more efficient algorithm for building the factor lattice of the fuzzy attribute-oriented concept lattice. A comparison between our approach and the existing algorithms is presented.

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

[2]  Gerd Stumme,et al.  Efficient Data Mining Based on Formal Concept Analysis , 2002, DEXA.

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

[4]  Anna Formica.  Concept Similarity in Fuzzy Formal Concept Analysis for Semantic Web , 2010, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[5]  Gabriel Ciobanu,et al.  Similarity relations in fuzzy attribute-oriented concept lattices , 2015, Fuzzy Sets Syst..

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

[7]  Ramón Fuentes-González,et al.  The use of two relations in L-fuzzy contexts , 2015, Inf. Sci..

[8]  Andrei Popescu,et al.  A general approach to fuzzy concepts , 2004, Math. Log. Q..

[9]  Denys Poshyvanyk,et al.  Combining Formal Concept Analysis with Information Retrieval for Concept Location in Source Code , 2007, 15th IEEE International Conference on Program Comprehension (ICPC '07).

[10]  Vincenzo Loia,et al.  Hierarchical web resources retrieval by exploiting Fuzzy Formal Concept Analysis , 2012, Inf. Process. Manag..

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

[12]  Radim Belohlávek,et al.  Grouping fuzzy sets by similarity , 2009, Inf. Sci..

[13]  Christian Lindig.  Fast Concept Analysis , 2000 .

[14]  Andrei Popescu,et al.  Non-dual fuzzy connections , 2004, Arch. Math. Log..

[15]  R. P. Dilworth,et al.  Residuated Lattices. , 1938, Proceedings of the National Academy of Sciences of the United States of America.

[16]  R. Belohlávek,et al.  Algorithms for fuzzy concept lattices , 2002 .

[17]  Jesús Medina,et al.  Relating attribute reduction in formal, object-oriented and property-oriented concept lattices , 2012, Comput. Math. Appl..

[18]  Ivo Düntsch,et al.  Modal-style operators in qualitative data analysis , 2002, 2002 IEEE International Conference on Data Mining, 2002. Proceedings..

[19]  Bernhard Ganter,et al.  Formal Concept Analysis, 6th International Conference, ICFCA 2008, Montreal, Canada, February 25-28, 2008, Proceedings , 2008, International Conference on Formal Concept Analysis.

[20]  Bernhard Ganter,et al.  Pattern Structures and Their Projections , 2001, ICCS.

[21]  Amedeo Napoli,et al.  Mining gene expression data with pattern structures in formal concept analysis , 2011, Inf. Sci..

[22]  Gerd Stumme,et al.  Computing iceberg concept lattices with T , 2002, Data Knowl. Eng..

[23]  Jan Konecny,et al.  Block Relations in Fuzzy Setting , 2011, CLA.

[24]  Stanislav Krajci,et al.  The Basic Theorem on Generalized Concept Lattice , 2004, CLA.

[25]  Manuel Ojeda-Aciego,et al.  Formal concept analysis via multi-adjoint concept lattices , 2009, Fuzzy Sets Syst..

[26]  Lotfi A. Zadeh,et al.  Quantitative fuzzy semantics , 1971, Inf. Sci..

[27]  Gabriel Ciobanu,et al.  A Formal Topology of Web Classification , 2014, ICCS.

[28]  Rudolf Wille,et al.  A Triadic Approach to Formal Concept Analysis , 1995, ICCS.

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

[30]  Rudolf Wille,et al.  Restructuring Lattice Theory: An Approach Based on Hierarchies of Concepts , 2009, ICFCA.

[31]  Ling Wei,et al.  Relation between concept lattice reduction and rough set reduction , 2010, Knowl. Based Syst..

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

[33]  Rudolf Wille,et al.  Methods of Conceptual Knowledge Processing , 2006, ICFCA.

[34]  Gabriel Ciobanu,et al.  Extracting Threshold Conceptual Structures from Web Documents , 2014, ICCS.

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

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

[37]  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..