The Structure of Concept Lattice Based on Matroidal Approach
Keywords:
matroid, bipartite graph, concept lattice,Abstract
For a context, using an inducing bipartite graph, this paper provides a character-ization for a concept and establishes a matroid. Further, with the assistance of thismatroid, this paper seeks out the lattice structure of all the concepts with a hierarchicalorder. All these results shows the potential and merit in using matroidal approachesfor designing and studying concept lattice.References
R.Wille, Restructuring lattice theory: an approach based on hierarchies of concepts, in:
I.Rival (Eds.), Ordered Sets, Dordrecht Boston, Reidel, 1982, pp.445-470.
C.Carpineto, G.Romano, Concept Data Analysis: Theory and Applications, John Wiley
& Sons Ltd., England, 2004.
B.Ganter, R.Wille, Formal Concept Analysis: Mathematical Foundations, Springer-
Verlag Berlin, Heidelberg, 1999. (German vesion: Springer, Heidelberg, 1996)
B.Ganter, G.Stumme, R.Wille, Formal Concept Analysis: Foundations and Applica-
tions, Springer-Verlag Berlin, Heidelberg, 2005.
K.Bertet, The dependence graphof a lattice, in: L.Szathmary, U.Priss (Eds.), CLA 2012,
M¶alaga, (Universidad de Ma¶alaga, Dept. Matem¶atica Aplicada), 2012, pp.223-231.
U.Priss, Formal concept analysis in information science, Annu. Rev. of Inf. Sci. and
Technol., 40(2006)521-543.
H.Whitney, On the abstract properties of linear dependence, Am. J. of Math., 57(3)
(1935)509-533.
H.Mao, The relation between matroid and concept lattice, Adv. in Math.(China),
(3)(2006)361-365.(in Chinese with English summary)
H.Mao, On closure axioms for a matroid using Galois connections, Math. Commun.,
(2)(2009)425-432.
H.Mao, On lattice-theoretical construction of matroids, Annu. of the Alexandru Ioan
Cuza Univ.-Math., 59(1)(2013)201-208.
H.Mao, Characterization and reduction of concept lattices through matroid theory, Inf.
Sci., 281(10)( 2014) 338-354.
Abello J, Pogel A J, Miller L. Breadth ¯rst search graph partitions and concept lattices.
J. of Univer. Comput. Sci., 10(8)(2004)934-954.
A.Berry, A.Sigayret, Representing a concept lattice by a graph., Discret. Appl. Math.,
(1-2)(2004)27-42.
A.Berry, J.Bordat, A.Sigayret, A local approach to concept generation, Annu. of Math.
and Artif. Intell., 49(1-4)(2007)117-136.
H.Mao, Representing a concept lattice by neighborly ideas, Annu. Univ. de Vest,
Timis.oara Ser. Mate.-Inf., 50(1)(2012)77-82.
D.J.A.Welsh, Matroid Theory, Academic Press, London, 1976.
Asian Journal of Computer and Information Systems (ISSN: 2321 – 5658)
G.GrÄatzer, Lattice Theory: Foundation, BirkhÄauser, Basel, 2011.
J.Oxley, Matroid Theory, 2nd. ed., Oxford University Press, New York, 2011.
J.A.Bondy, U.S.R.Murty, Graph Theory with Applications, Elsevier Science Publishing
Co. Inc., New York, 1976.
R.Wille, Boolean concept logic, in: B.Ganter, G.W.Minean (Eds.), ICCS 2000,
Springer-Verlag Berlin, Heidelberg, 2000, pp.317-331.
B.Vormbrock, R.Wille, Semiconcept and protoconcept algebras: the basic theorems,
in: B.Ganter et al. (Eds.), Formal Concept Analysis: Foundations and Applications,
Springer-Verlag Berlin, Heidelberg, 2005, pp.34-48.
Asian Journal of Computer and Information Systems (ISSN: 2321 – 5658)
Volume 03– Issue 03, August 2015
Asian
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