Decision algorithms and flow graphs; a rough set approach
DOI:
https://doi.org/10.26636/jtit.2003.3.185Keywords:
rough sets, decision algorithms, flow graphs, data miningAbstract
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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References
[1] J. M. Bernardo and A. F. M. Smith, Bayesian Theory. Chichester [etc.]: Wiley, 1994 (Wiley series in probability and mathematical statistics).
View in Google Scholar
[2] G. E. P. Box and G. C. Tiao, Bayesian Inference in Statistical Analysis. New York [etc.]: Wiley, 1992.
View in Google Scholar
[3] M. Berthold and D. J. Hand, Intelligent Data Analysis - an Introduction. Berlin: Springer, 1999.
View in Google Scholar
[4] L. R. Ford and D. R. Fulkerson, Flows in Networks. Princeton [etc.]: Princeton University Press, 1962.
View in Google Scholar
[5] J. Łukasiewicz, "Die logischen Grundlagen der Wahrscheinlichkeitsrechnung" (Kraków, 1913) in Jan Łukasiewicz - Selected Works, L. Borkowski, Ed. Amsterdam [etc.]: North Holland Publ., Warsaw: Polish Scientific Publ., 1970.
View in Google Scholar
[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.
View in Google Scholar
[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.
View in Google Scholar
[8] Z. Pawlak, "Rough sets, decision algorithms and Bayes' theorem", Eur. J. Oper. Res., vol. 136, pp. 181-189, 2002.
View in Google Scholar
[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.
View in Google Scholar
[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.
View in Google Scholar
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Copyright (c) 2003 Journal of Telecommunications and Information Technology
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