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Decisions algorithms and flow graphs; a rough set approach

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EN
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EN
This paper concerns some relationship between Bayes' theorem and rough sets. It is revealed that any decision algorithm satisfies Bayes' theorem, without referring to either prior or posterior probabilities inherently associated with classical Bayesian methodology. This leads to a new simple form of this theorem, which results in new algorithms and applications. Besides, it is shown that with every decision algorithm a flow graph can be associated. Bayes' theorem can be viewed as a flow conservation rule of information flow in the graph. Moreover, to every flow graph the Euclidean space can be assigned. Points of the space represent decisions specified by the decision algorithm, and distance between points depicts distance between decisions in the decision algorithm.
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Tom
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98--101
Opis fizyczny
Bibliogr. 10 poz., tab., rys.
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Bibliografia
  • [1] J. M. Bernardo and A. F. M. Smith, Bayesian Theory. Chichester [etc.]: Wiley, 1994 (Wiley series in probability and mathematical statistics).
  • [2] G. E. P. Box and G. C. Tiao, Bayesian Inference in Statistical Analysis. New York [etc.]: Wiley, 1992.
  • [3] M. Berthold and D. J. Hand, Intelligent Data Analysis – an Introduction. Berlin: Springer, 1999.
  • [4] L. R. Ford and D. R. Fulkerson, Flows in Networks. Princeton [etc.]: Princeton University Press, 1962.
  • [5] J. Łukasiewicz, “Die logishen Grundlagen der Wahrscheinilchkeit srechnung” (Kraków, 1913) in Jan Łukasiewicz – Selected Works, L. Borkowski, Ed. Amsterdam [etc.]: North Holland Publ., Warsaw: Polish Scientific Publ., 1970.
  • [6] S. Greco, Z. Pawlak, and R. Słowiński, “Generalized decision algorithms, rough inference rules and flow graphs” in Rough Sets and Current Trends in Computing, J. J. Alpigini, J. F. Peters, A. Skowron, and N. Zhong, Eds., Lecture Notes in Artificial Intelligence. Berlin: Springer, 2002, vol. 2475, pp. 93–104.
  • [7] Z. Pawlak, “In pursuit of patterns in data reasoning from data – the rough set way” in Rough Sets and Current Trends in Computing, J. J. Alpigini, J. F. Peters, A. Skowron, and N. Zhong, Eds., Lecture Notes in Artificial Intelligence. Berlin: Springer, 2002, vol. 2475, pp. 1–9.
  • [8] Z. Pawlak, “Rough sets, decision algorithms and Bayes’ theorem”, Eur. J. Oper. Res., vol. 136, pp. 181–189, 2002.
  • [9] S. Tsumoto and H. Tanaka, “Discovery of functional components of proteins based on PRIMEROSE and domain knowledge hierarchy” in Proc. Worksh. Rough Sets & Soft Comput. RSSC-94, T. Y. Lin and A. M. Wildberger, Eds., Soft Computing, SCS, 1995, pp. 280–285.
  • [10] S. K. M. Wong and W. Ziarko, “Algorithm for inductive learning”, Bull. Polish Acad. Sci., vol. 34, no. 5-6, pp. 271–276, 1986.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPS2-0021-0041
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