On heterogeneous formal contexts

We propose a new type of fuzzification for formal concept analysis that works with heterogeneous values in a context and illustrate this with an example. We formulate and prove an appropriate counterpart to the so-called basic theorem of a concept lattice. We show that this is a generalization of the previous approaches: it covers the so-called generalized concept lattice and multi-adjoint t-concept lattices.

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

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

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

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

[5]  Radim Belohlávek,et al.  Crisply Generated Fuzzy Concepts , 2005, ICFCA.

[6]  Manuel Ojeda-Aciego,et al.  Multi-adjoint Logic Programming with Continuous Semantics , 2001, LPNMR.

[7]  Giangiacomo Gerla,et al.  Similarity-based Unification , 2000, Fundam. Informaticae.

[8]  A. Jaoua,et al.  Discovering knowledge from fuzzy concept lattice , 2001 .

[9]  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..

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

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

[12]  Jesús Medina,et al.  Multi-adjoint t-concept lattices , 2010, Inf. Sci..

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

[14]  Jozef Pócs.  On possible generalization of fuzzy concept lattices using dually isomorphic retracts , 2012, Inf. Sci..

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

[16]  Radim Belohlávek,et al.  Sup-t-norm and inf-residuum are one type of relational product: Unifying framework and consequences , 2012, Fuzzy Sets Syst..

[17]  Stanislav Krajci,et al.  Relationship between Two FCA Approaches on Heterogeneous Formal Contexts , 2012, CLA.

[18]  Gerd Stumme,et al.  Begriffliche Wissensverarbeitung: Methoden und Anwendungen , 2000 .

[19]  Manuel Ojeda-Aciego,et al.  On multi-adjoint concept lattices based on heterogeneous conjunctors , 2012, Fuzzy Sets Syst..

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

[21]  Silke Pollandt.  Datenanalyse mit Fuzzy-Begriffen , 2000 .

[22]  Stanislav Krajci.  Every Concept Lattice With Hedges Is Isomorphic To Some Generalized Concept Lattice , 2005, CLA.

[23]  Jozef Pócs,et al.  Note on generating fuzzy concept lattices via Galois connections , 2012, Inf. Sci..

[24]  Jesús Medina,et al.  A comparative study of adjoint triples , 2013, Fuzzy Sets Syst..

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