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Rough Sets and Infomorphisms: Towards Approximation of Relations in Distributed Environments

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EN
Abstrakty
EN
We discuss the relationships between information systems and classifications as well as between infomorphisms and definability of relations (between whole objects and their parts) in information systems. Infomorphisms between information systems (classifications) IS1 and IS2 make it possible to define some formulas over IS2 by means of formulas over IS1. The remaining formulas over IS2 can be approximatively defined by means of formulas over IS1. The approximation operations are defined using the rough set approach. We present definitions and examples of such approximations.
Wydawca
Rocznik
Strony
263--277
Opis fizyczny
tab., bibliogr. 25 poz.
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autor
autor
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Bibliografia
  • [1] Barr M.: Autonomous Categories, Lecture Notes in Mathematics 752, Springer-Verlag, Heidelberg 1979.
  • [2] Barwise, J., Seligman, J.: Information Flow: The Logic of Distributed Systems, Cambridge University Press Tracts in Theoretical Computer Science 44, 1997.
  • [3] Gamma, E., Helm, R., Johnson, R., Vlissides, J.: Design Patterns: Elements of Reusable Object-Oriented Software, London, Addison-Wesley, 1995.
  • [4] Doherty, P., Łukaszewicz, W., Skowron, A., Szałas, A.: Combining rough and crisp knowledge in deductive databases (to appear in [13]).
  • [5] Huhns, M.N., Singh, M.P. (Eds.): Readings in Agents. Morgan Kaufmann, San Mateo, 1998.
  • [6] WEB page for Chu spaces http://chu.stanford.edu/
  • [7] Komorowski, J., Pawlak, Z., Polkowski, L., Skowron, A.: Rough Sets: A Tutorial. In [8], 3-98, 1999.
  • [8] Pal, S.K., Skowron, A. (Eds.): Rough-Fuzzy Hybridization A New Trend in Decision Making, Springer–Verlag, Singapore, 1999.
  • [9] Pawlak, Z.: Mathematical Foundations of Information Retrieval, Proceedings of Symposium of Mathematical Foundations of Computer Science, September 3-8, 1973, High Tartras, 135-136; see also: Mathematical Foundations of Information Retrieval, CC PAS Report 101, 1973.
  • [10] Pawlak, Z.: Information Systems, ICS PAS Report 338, 1979.
  • [11] Pawlak, Z.: Information Systems: Theoretical Foundations, WNT Warsaw, 1983 (in Polish).
  • [12] Pawlak, Z.: Rough Sets. Theoretical Aspects of Reasoning about Data, Kluwer Academic Publishers, Dordrecht, 1991.
  • [13] Pal, S.K., Polkowski, L., Skowron, A. (Eds.): Rough-Neuro Computing: Techniques for Computing with Words. Springer-Verlag, Berlin, 2003. (to appear).
  • [14] Pal, S.K., Peters, J.F., Polkowski, L., Skowron, A., Rough-Neuro Computing: An Introduction, in: [13], 16-43.
  • [15] Peters, J.F., Skowron, A., Stepaniuk, J., Ramanna, S.: Towards an Ontology of Approximate Reason, Fundamenta Informaticae 51(1-2), 2002, 157-173.
  • [16] Polkowski, L., Skowron, A. (Eds.): Rough Sets in Knowledge Discovery 1-2, Studies in Fuzziness and Soft Computing 18-19, Physica-Verlag, Heidelberg, 1998.
  • [17] Polkowski, L., Skowron, A.: Rough Mereological Foundations for Design, Analysis, Synthesis, and Control in Distributed Systems, Information Sciences An International Journal 104(1-2), 1998, 129-156.
  • [18] Polkowski, L., Skowron, A.: Towards Adaptive Calculus of Granules, In: [24] 1, 201-227.
  • [19] Pratt, V.R.: Types as Processes, via Chu Spaces, Electronic Notes in Theoretical Computer Science 7, 1997, 1-21, http://www.elsevier.nl/locate/volume7.html.
  • [20] Skowron, A.: Rough sets in KDD. in: Z. Shi, B. Faltings, and M. Musem (Eds.), 16-th World Computer Congress (IFIP’2000): Proceedings of Conference on Intelligent Information Processing (IIP’2000), Publishing House of Electronic Industry, Beijing, 2000, 1-17.
  • [21] Skowron, A.: Toward Intelligent Systems: Calculi of Information Granules. Bulletin of the International Rough Set Society 5(1-2), 2001, 9-30.
  • [22] Skowron, A., Stepaniuk, J.: Information Granules: Towards Foundations of Granular Computing, International Journal of Intelligent Systems 16(1), 2001, 57-86.
  • [23] Skowron, A., Stepaniuk, J.: Information Granules and Rough-Neuro Computing. (to appear in [13]).
  • [24] Zadeh, L.A., Kacprzyk, J. (Eds.): Computing with Words in Information/Intelligent Systems 1-2, Studies in Fuzziness and Soft Computing 30, Physica–Verlag, Heidelberg, 1999.
  • [25] Zadeh, L.A.: A New Direction in AI: Toward a Computational Theory of Perceptions, AI Magazine 22(1), 2001, 73–84.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS2-0004-0094
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