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A Macroscopic Approach to FCA and Its Various Fuzzifications

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Part of the Lecture Notes in Computer Science book series (LNAI,volume 7278)

Abstract

We promote biresiduation as a fundamental unifying principle in Formal Concept Analysis, including fuzzification and factor analysis. In particular, we show that maximal formal rectangles are exactly formal concepts within the presented framework of biresiduated maps on ordered sets. Macroscopic implications yield the particular derivation operators in specific settings such as Fuzzy Formal Concept Analysis, Factor Analysis, and degree of containment (i.e. degree of being a subset).

Keywords

  • biresiduation
  • complete monoids
  • formal concept analysis
  • fuzzy formal concept analysis
  • factor analysis
  • linear algebra

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References

  1. Belohlavek, R.: Optimal decompositions of matrices with entries from residuated lattices. Journal of Logic and Computation (2011)

    Google Scholar 

  2. Belohlavek, R.: What is a Fuzzy Concept Lattice? II. In: Kuznetsov, S.O., Ślęzak, D., Hepting, D.H., Mirkin, B.G. (eds.) RSFDGrC 2011. LNCS, vol. 6743, pp. 19–26. Springer, Heidelberg (2011)

    CrossRef  Google Scholar 

  3. Blyth, T.: Lattices and Ordered Algebraic Structures. Universitext, Springer (2005)

    Google Scholar 

  4. Belohlávek, R., Vychodil, V.: What is a fuzzy concept lattice? In: Snás̃el, V., Bělohlávek, R. (eds.) Proc. CLA 2005. CEUR WS, vol. 162, pp. 34–45. Palacký University in Olomouc, VŠB–Technical University of Ostrava (2005)

    Google Scholar 

  5. Belohlavek, R., Vychodil, V.: Factor Analysis of Incidence Data via Novel Decomposition of Matrices. In: Ferré, S., Rudolph, S. (eds.) ICFCA 2009. LNCS, vol. 5548, pp. 83–97. Springer, Heidelberg (2009)

    CrossRef  Google Scholar 

  6. Droste, M., Kuich, W., Vogler, H.: Handbook of Weighted Automata. Monographs in Theoretical Computer Science. Springer (2009)

    Google Scholar 

  7. Davey, B.A., Priestley, H.A.: Introduction to lattices and order. Cambridge University Press, Cambridge (1990)

    MATH  Google Scholar 

  8. Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, Heidelberg (1999)

    CrossRef  MATH  Google Scholar 

  9. Krajci, S.: The basic theorem on generalized concept lattice. In: Snásel, V., Belohlávek, R. (eds.) CLA. CEUR Workshop Proceedings, vol. 110. CEUR-WS.org (2004)

    Google Scholar 

  10. Medina, J., Ojeda-Aciego, M.: On the representation theorem of multi-adjoint concept lattices. In: Carvalho, J.P., Dubois, D., Kaymak, U., da Costa Sousa, J.M. (eds.) IFSA/EUSFLAT Conf., pp. 1091–1095 (2009)

    Google Scholar 

  11. Medina, J., Ojeda-Aciego, M., Ruiz-Calviño, J.: Formal concept analysis via multi-adjoint concept lattices. Fuzzy Sets and Systems 160(2), 130–144 (2009)

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 2012 Springer-Verlag Berlin Heidelberg

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Kaiser, T.B., Schmidt, S.E. (2012). A Macroscopic Approach to FCA and Its Various Fuzzifications. In: Domenach, F., Ignatov, D.I., Poelmans, J. (eds) Formal Concept Analysis. ICFCA 2012. Lecture Notes in Computer Science(), vol 7278. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29892-9_16

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  • DOI: https://doi.org/10.1007/978-3-642-29892-9_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29891-2

  • Online ISBN: 978-3-642-29892-9

  • eBook Packages: Computer ScienceComputer Science (R0)