Formal concept analysis via multi-adjoint concept lattices

Several fuzzifications of formal concept analysis have been proposed to deal with uncertain information. In this paper, we focus on concept lattices under a multi-adjoint paradigm, which enriches the language providing greater flexibility to the user in that he/she can choose from a number of different connectives. Multi-adjoint concept lattices are shown to embed different fuzzy extensions of concept lattices found in the literature, the main results of the paper being the representation theorem of this paradigm and the embedding of other well-known approaches.

[1]  Jean-Marc Champarnaud,et al.  Theoretical study and implementation of the canonical automaton , 2002, Fundam. Informaticae.

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

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

[4]  Nehad N. Morsi,et al.  Associatively tied implications , 2003, Fuzzy Sets Syst..

[5]  Ginés Moreno,et al.  On fuzzy unfolding: A multi-adjoint approach , 2005, Fuzzy Sets Syst..

[6]  Vilém Vychodil,et al.  What is a fuzzy concept lattice? , 2005, CLA.

[7]  Manuel Ojeda-Aciego,et al.  Similarity-based unification: a multi-adjoint approach , 2004, EUSFLAT Conf..

[8]  Radim Belohlávek,et al.  What is a Fuzzy Concept Lattice? II , 2011, RSFDGrC.

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

[10]  Angus Macintyre,et al.  Trends in Logic , 2001 .

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

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

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

[14]  Stanislav Krajci,et al.  A Generalized Concept Lattice , 2005, Log. J. IGPL.

[15]  Andrei Popescu,et al.  Concept lattices and similarity in non-commutative fuzzy logic , 2002, Fundam. Informaticae.

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

[17]  Andrei Popescu,et al.  Non-commutative fuzzy Galois connections , 2003, Soft Comput..

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

[19]  Ramón Fuentes-González,et al.  Concept lattices defined from implication operators , 2000, Fuzzy Sets Syst..

[20]  Manuel Ojeda-Aciego,et al.  Towards Biresiduated Multi-adjoint Logic Programming , 2003, CAEPIA.

[21]  Jesús Medina.  Towards Multi-adjoint Property-Oriented Concept Lattices , 2010, RSKT.

[22]  Andrei Popescu,et al.  Similarity Convergence in Residuated Structures , 2005, Log. J. IGPL.

[23]  Radim Bělohlávek,et al.  Lattices of Fixed Points of Fuzzy Galois Connections , 2001 .

[24]  Manuel Ojeda-Aciego,et al.  On Multi-adjoint Concept Lattices: Definition and Representation Theorem , 2007, ICFCA.

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