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).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Belohlavek, R.: Optimal decompositions of matrices with entries from residuated lattices. Journal of Logic and Computation (2011)
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)
Blyth, T.: Lattices and Ordered Algebraic Structures. Universitext, Springer (2005)
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)
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)
Droste, M., Kuich, W., Vogler, H.: Handbook of Weighted Automata. Monographs in Theoretical Computer Science. Springer (2009)
Davey, B.A., Priestley, H.A.: Introduction to lattices and order. Cambridge University Press, Cambridge (1990)
Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, Heidelberg (1999)
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)
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)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
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)