Abstract
The paper makes the first attempt to combine two methodologies concerning uncertainty and fuzzy reasoning, namely rough set flow graphs and fuzzy relation equations. Rough set flow graphs proposed by Z. Pawlak are a useful tool for the knowledge representation. In this paper, we use them to represent the knowledge of transitions between states included in multistage dynamic information systems. The knowledge represented by flow graphs is a basis for determining possibilities of appearances of states in the future using the max − * fuzzy composition. In the approach proposed in the paper, we take advantage of some properties of the max − * fuzzy relation equations.
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Butz, C.J., Yan, W., Yang, B.: The Computational Complexity of Inference Using Rough Set Flow Graphs. In: Ślęzak, D., Wang, G., Szczuka, M.S., Düntsch, I., Yao, Y. (eds.) RSFDGrC 2005. LNCS (LNAI), vol. 3641, pp. 335–344. Springer, Heidelberg (2005)
Drewniak, J.: Fuzzy Relation Equations and Inequalities. Fuzzy Sets and Systems 14(3), 237–247 (1984)
Drewniak, J.: Fuzzy Relation Calculus. University of Silesia, Katowice (1989)
Greco, S., Pawlak, Z., Słowiński, R.: Generalized Decision Algorithms, Rough Inference Rules, and Flow Graphs. In: Alpigini, J.J., et al. (eds.) RSCTC 2002. LNCS (LNAI), vol. 2475, pp. 93–104. Springer, Heidelberg (2002)
Lee, K.H.: First Course on Fuzzy Theory and Applications. Springer, Heidelberg (2005)
Matusiewicz, Z.: Fuzzy relation equations of type max-* for Lukasiewicz conjunction. Scientific Bulletin of Chelm, Section of Mathematics and Computers Science 1/07, 83–86 (2007)
Matusiewicz, Z.: Properties of fuzzy relation equations of type max-* for some classes of triangular norm conjunctions. In: Klement, E.P., et al. (eds.) Proc. of the FSTA 2008, Liptovsky Jan, Slovak Republic, p. 80 (2008)
Pancerz, K.: Extensions of Dynamic Information Systems in State Prediction Problems: the First Study. In: Magdalena, L., Ojeda-Aciego, M., Verdegay, J.L. (eds.) Proc. of the IPMU 2008, Malaga, Spain, pp. 101–108 (on CD, 2008)
Pawlak, Z.: Rough Sets - Theoretical Aspects of Reasoning About Data. Kluwer Academic Publishers, Dordrecht (1991)
Pawlak, Z.: Flow Graphs and Data Mining. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets III. LNCS, vol. 3400, pp. 1–36. Springer, Heidelberg (2005)
Sanchez, E.: Resolution of composite fuzzy relation equations. Information Control 30, 38–48 (1976)
Suraj, Z.: The Synthesis Problem of Concurrent Systems Specified by Dynamic Information Systems. In: Polkowski, L., Skowron, A. (eds.) Rough Sets in Knowledge Discovery 2, pp. 418–448. Physica-Verlag, Berlin (1998)
Suraj, Z., Pancerz, K.: Flow Graphs as a Tool for Mining Prediction Rules of Changes of Components in Temporal Information Systems. In: Yao, J., et al. (eds.) RSKT 2007. LNCS (LNAI), vol. 4481, pp. 468–475. Springer, Heidelberg (2007)
Zhang, C., Lu, C., Li, D.: On perturbation properties of fuzzy relation equations. J. Fuzzy Math. 14(1), 53–63 (2006)
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Matusiewicz, Z., Pancerz, K. (2008). Rough Set Flow Graphs and Max − * Fuzzy Relation Equations in State Prediction Problems. In: Chan, CC., Grzymala-Busse, J.W., Ziarko, W.P. (eds) Rough Sets and Current Trends in Computing. RSCTC 2008. Lecture Notes in Computer Science(), vol 5306. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88425-5_37
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DOI: https://doi.org/10.1007/978-3-540-88425-5_37
Publisher Name: Springer, Berlin, Heidelberg
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