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Galois Connections and Data Analysis

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We investigate Galois connections and their relations to the major theories of (qualitative) data analysis: Rough Set Theory (RST), Formal Concept Analysis (FCA) and John Stuart Mill Reasoning (JSM-Reasoning). Polarities, a type of contravariant Galois connections, and their relationships with data analysis has been already well-known. This paper shows how axialities, a type of covariant Galois connections, are related to problems adressed by data analysis and prove that they give rise to a number of interesting lattices.
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401--415
Opis fizyczny
Bibliogr. 12 poz.
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Bibliografia
  • [1] Düntch, I. and Gediga, G. (2002), Modal-style operators in qualitative data analysis, in Proceedings of the 2002 I EE Conference on Data Mining (ICDM'2002), pp. 155-162.
  • [2] Düntch, I. and Gediga, G. (2003), Approximation operators in qualitative data analysis, in de Swart, H.. Orłowska, E., Schmidt. G., Roubens, M., (eds). Theory and Applications of Relational Structures as Knowledge Instruments, Lecture Notes in Computer Science, pp 216-233. Springer Verlag, Heidelberg.
  • [3] Erne, M., Koslowski, J., Melton, A. and Strecker, G. E. (1991), A primer on Galois connections, http://www.math.ksu.edu/~strecker/primer.ps
  • [4] Finn. V. K. (1989), On axiomatization of many-valued logics associated with formalizatioin of plausible reasoning. Studia Lógica, 42/4, pp. 423-447.
  • [5] Finn, V. K. (1999), On the synthesis of cognitive procedures and the problem of induction, NTl Series, 1-2. pp. 8-45.
  • [6] Grigoriev, P., Kuznetsov, S., Obiedkov, S. and Yevtushenko, S. (2002), On a version of Mill's method of difference, in Proceedings of the 15th Conference on Artificial Intelligence (ECAI'2002), pp. 26-31.
  • [7] Kent, R. (1996). Rough concept analysis: a synthesis of rough sets and formal concept analysis. Fundamenta Informaticae, 27(2/3), pp. 169-181.
  • [8] Monjardet. D. (1970). Tresses, fuseaux, préorderes et topologiex. Mathématique et Sciences Humaines, 30. pp. 11-22.
  • [9] Orłowska, E. (1995). Information algebras, in Alagar. V. S. and Nivat. M., (Eds), Algebraic Methodology and Software Technology. 4th International Conference (AMASt’95), Montreal. Canada. Proceedings, Lecture Notes in Computer Science, vol 369. pp. 50-65, Springer-Verlag.
  • [10] Pagliani. P. (1993), From concept lattices to approximation spaces: algebraic structures of some spaces of partial objects. Fundamenta Informaticae. 18, pp. 1-25.
  • [11] Pawlak, Z. (1982), Rough sets. The International Journal of Computer and Information Science, 11. pp. 341-356.
  • [12] Wille, R. (1982), Reconstructing lattice theory: An approach based on hierachies of concepts, in Rival, I. (Ed.), Ordered Sets, NATO Advanced Studies Institute, pp. 445-470, Dodrecht: Reidel.
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bwmeta1.element.baztech-article-BUS2-0005-0047
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