Application of the L-fuzzy concept analysis in the morphological image and signal processing

In this work we are going to set up a new relationship between the L-fuzzy Concept Analysis and the Fuzzy Mathematical Morphology. Specifically we prove that the problem of finding fuzzy images or signals that remain invariant under a fuzzy morphological opening or under a fuzzy morphological closing, is equal to the problem of finding the L-fuzzy concepts of some L-fuzzy context. Moreover, since the Formal Concept Analysis and the Mathematical Morphology are the particular cases of the fuzzy ones, the showed result has also an interpretation for binary images or signals.

[1]  Ramón Fuentes-González,et al.  Treatment of L-Fuzzy contexts with absent values , 2009, Inf. Sci..

[2]  Ramón Fuentes-González,et al.  Analysis of certain L-Fuzzy Relational equations and the Study of its solutions by Means of the L-Fuzzy Concept Theory , 2012, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[3]  Marta Elena del Socorro Millán.  Descubrimiento de Conocimiento en Bases de Datos , 2009 .

[4]  R. Belohlávek.  Fuzzy Closure Operators , 2001 .

[5]  Henk J. A. M. Heijmans,et al.  Fundamenta Morphologicae Mathematicae , 2000, Fundam. Informaticae.

[6]  Radim Belohlávek,et al.  Concept lattices of isotone vs. antitone Galois connections in graded setting: Mutual reducibility revisited , 2012, Inf. Sci..

[7]  Václav Snásel,et al.  FCA as a Tool for Inaccuracy Detection in Content-Based Image Analysis , 2010, 2010 IEEE International Conference on Granular Computing.

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

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

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

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

[12]  Petros Maragos,et al.  Lattice Image Processing: A Unification of Morphological and Fuzzy Algebraic Systems , 2005, Journal of Mathematical Imaging and Vision.

[13]  G. Matheron.  Random Sets and Integral Geometry , 1976 .

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

[15]  Ramón Fuentes-González,et al.  Construction of the L-fuzzy concept lattice , 1998, Fuzzy Sets Syst..

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

[17]  H. Heijmans.  Morphological image operators , 1994 .

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

[19]  Ramón Fuentes-González,et al.  Inclusion grade and fuzzy implication operators , 2000, Fuzzy Sets Syst..

[20]  Noé N. Frago,et al.  Descubrimiento de Conocimiento en Bases de Datos Utilizando Técnicas de Morfología Matemática Borrosa , 2007 .

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

[22]  Henri Prade,et al.  Interval-Valued Fuzzy Galois Connections: Algebraic Requirements and Concept Lattice Construction , 2010, Fundam. Informaticae.

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

[24]  Jesús Medina,et al.  Multi-adjoint property-oriented and object-oriented concept lattices , 2012, Inf. Sci..

[25]  Jean Serra,et al.  Image Analysis and Mathematical Morphology , 1983 .

[26]  G. Matheron.  Éléments pour une théorie des milieux poreux , 1967 .

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

[28]  Michal Baczynski,et al.  Fuzzy Implications , 2008, Studies in Fuzziness and Soft Computing.

[29]  Isabelle Bloch,et al.  Fuzzy mathematical morphologies: A comparative study , 1995, Pattern Recognit..

[30]  Pierre Soille,et al.  Morphological Image Analysis: Principles and Applications , 2003 .

[31]  Joan Torrens,et al.  S-implications and R-implications on a finite chain , 2004, Kybernetika.

[32]  Pierre Soille,et al.  Morphological Image Analysis , 1999 .

[33]  Bernard De Baets,et al.  A Fuzzy Morphology: a Logical Approach , 1998 .

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

[35]  Ramón Fuentes-González,et al.  Generation of fuzzy mathematical morphologies , 2001 .

[36]  P. Burillo,et al.  PROCESOS DE DESCUBRIMIENTO DE CONOCIMIENTO EN BASES DE DATOS USANDO GRAFOS ASOCIADOS A FILTROS MORFOLÓGICOS , 2008 .

[37]  Ramón Fuentes-González.  The incorporation of the Mathematical Morphology , the Formal Concept Analysis and the Fuzzy Logic techniques and tools to the data cleaning , aggregating , reducing and mining stages of the Knowledge Discovery process TIC 2003-08693 , 2005 .

[38]  Isabelle Bloch,et al.  Duality vs. adjunction for fuzzy mathematical morphology and general form of fuzzy erosions and dilations , 2009, Fuzzy Sets Syst..