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On Representation and Analysis of Crisp and Fuzzy Information Systems

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Transactions on Rough Sets VI

Part of the book series: Lecture Notes in Computer Science ((TRS,volume 4374))

Abstract

This paper proposes an approach to representation and analysis of information systems with fuzzy attributes, which combines the variable precision fuzzy rough set (VPFRS) model with the fuzzy flow graph method. An idea of parameterized approximation of crisp and fuzzy sets is presented. A single ε-approximation, which is based on the notion of fuzzy rough inclusion function, can be used to express the crisp approximations in the rough set and variable precision rough set (VPRS) model. A unified form of the ε-approximation is particularly important for defining a consistent VPFRS model. The introduced fuzzy flow graph method enables alternative description of decision tables with fuzzy attributes. The generalized VPFRS model and fuzzy flow graphs, taken together, can be applied to determining a system of fuzzy decision rules from process data.

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References

  1. Bandler, W., Kohout, L.: Fuzzy Power Sets and Fuzzy Implication Operators. Fuzzy Sets and Systems 4, 13–30 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  2. Burillo, P., Frago, N., Fuentes, R.: Inclusion Grade and Fuzzy Implication Operators. Fuzzy Sets and Systems 114, 417–429 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chen, S.M., Yeh, M.S., Hsiao, P.Y.: A Comparison of Similarity Measures of Fuzzy Values. Fuzzy Sets and Systems 72, 79–89 (1995)

    Article  MathSciNet  Google Scholar 

  4. Cornelis, C., Van der Donck, C., Kerre, E.: Sinha-Dougherty Approach to the Fuzzification of Set Inclusion Revisited. Fuzzy Sets and Systems 134, 283–295 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  5. De Baets, B., De Meyer, H., Naessens, H.: On Rational Cardinality-based Inclusion Measures. Fuzzy Sets and Systems 128, 169–183 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  6. Dubois, D., Prade, H.: Putting Rough Sets and Fuzzy Sets Together. In: Słowiński, R. (ed.) Intelligent Decision Support: Handbook of Applications and Advances of the Rough Sets Theory, pp. 203–232. Kluwer Academic Publishers, Dordrecht (1992)

    Google Scholar 

  7. Fernández Salido, J.M., Murakami, S.: Rough Set Analysis of a General Type of Fuzzy Data Using Transitive Aggregations of Fuzzy Similarity Relations. Fuzzy Sets and Systems 139, 635–660 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  8. Greco, S., Matarazzo, B., Słowiński, R.: Rough Set Processing of Vague Information Using Fuzzy Similarity Relations. In: Calude, C.S., Paun, G. (eds.) Finite Versus Infinite — Contributions to an Eternal Dilemma, pp. 149–173. Springer, Heidelberg (2000)

    Google Scholar 

  9. 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)

    Chapter  Google Scholar 

  10. Greco, S., Pawlak, Z., Słowiński, R.: Bayesian Confirmation Measures within Rough Set Approach. In: Tsumoto, S., et al. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 264–273. Springer, Heidelberg (2004)

    Google Scholar 

  11. Greco, S., Matarazzo, B., Słowiński, R.: Rough Membership and Bayesian Confirmation Measures for Parameterized Rough Sets. In: Ślęzak, D., et al. (eds.) RSFDGrC 2005. LNCS (LNAI), vol. 3641, pp. 314–324. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  12. Inuiguchi, M.: Generalizations of Rough Sets: From Crisp to Fuzzy Cases. In: Tsumoto, S., et al. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 26–37. Springer, Heidelberg (2004)

    Google Scholar 

  13. Katzberg, J.D., Ziarko, W.: Variable Precision Extension of Rough Sets. Fundamenta Informaticae 27, 155–168 (1996)

    MathSciNet  MATH  Google Scholar 

  14. Klir, G.J., Folger, T.A.: Fuzzy Sets, Uncertainty, and Information. Prentice-Hall, Englewood Cliffs (1988)

    MATH  Google Scholar 

  15. Lin, T.Y.: Coping with Imprecision Information — Fuzzy Logic. In: Downsizing Expo, Santa Clara Convention Center (1993)

    Google Scholar 

  16. Mieszkowicz-Rolka, A., Rolka, L.: Variable Precision Rough Sets: Evaluation of Human Operator’s Decision Model. In: Sołdek, J., Drobiazgiewicz, L. (eds.) Artificial Intelligence and Security in Computing Systems, pp. 33–40. Kluwer Academic Publishers, Dordrecht (2003)

    Google Scholar 

  17. Mieszkowicz-Rolka, A., Rolka, L.: Variable Precision Fuzzy Rough Sets Model in the Analysis of Process Data. In: Ślęzak, D., et al. (eds.) RSFDGrC 2005. LNCS (LNAI), vol. 3641, pp. 354–363. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  18. Nakamura, A.: Application of Fuzzy-Rough Classifications to Logics. In: Słowiński, R. (ed.) Intelligent Decision Support: Handbook of Applications and Advances of the Rough Sets Theory, pp. 233–250. Kluwer Academic Publishers, Dordrecht (1992)

    Google Scholar 

  19. Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991)

    MATH  Google Scholar 

  20. Pawlak, Z.: Decision Algorithms, Bayes’ Theorem and Flow Graphs. In: Rutkowski, L., Kacprzyk, J. (eds.) Advances in Soft Computing, pp. 18–24. Physica-Verlag, Heidelberg (2003)

    Google Scholar 

  21. 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)

    Chapter  Google Scholar 

  22. 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)

    Chapter  Google Scholar 

  23. Peters, J.F., Skowron, A. (eds.): Transactions on Rough Sets III. LNCS, vol. 3400. Springer, Heidelberg (2005)

    MATH  Google Scholar 

  24. Polkowski, L.: Toward Rough Set Foundations. Mereological Approach. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 8–25. Springer, Heidelberg (2004)

    Google Scholar 

  25. Radzikowska, A.M., Kerre, E.E.: A Comparative Study of Fuzzy Rough Sets. Fuzzy Sets and Systems 126, 137–155 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  26. Skowron, A., Stepaniuk, J.: Tolerance Approximation Spaces. Fundamenta Informaticae 27, 245–253 (1996)

    MathSciNet  MATH  Google Scholar 

  27. Ślęzak, D., Ziarko, W.: Variable Precision Bayesian Rough Set Model. In: Wang, G., et al. (eds.) RSFDGrC 2003. LNCS (LNAI), vol. 2639, pp. 312–315. Springer, Heidelberg (2003)

    Google Scholar 

  28. Ślęzak, D., Wang, G., Szczuka, M., Düntsch, I., Yao, Y. (eds.): RSFDGrC 2005. LNCS (LNAI), vol. 3641. Springer, Heidelberg (2005)

    Google Scholar 

  29. Ślęzak, D.: Rough Sets and Bayes Factor. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets III. LNCS, vol. 3400, pp. 202–229. Springer, Heidelberg (2005)

    Google Scholar 

  30. Słowiński, R. (ed.): Intelligent Decision Support: Handbook of Applications and Advances of the Rough Sets Theory. Kluwer Academic Publishers, Dordrecht (1992)

    MATH  Google Scholar 

  31. Tsumoto, S., et al. (eds.): RSCTC 2004. LNCS (LNAI), vol. 3066. Springer, Heidelberg (2004)

    MATH  Google Scholar 

  32. Yager, R.R., Filev, D.P.: Essentials of Fuzzy Modelling and Control. John Wiley & Sons, Chichester (1994)

    Google Scholar 

  33. Liu, W.N., Yao, J., Yao, Y.: Rough Approximations under Level Fuzzy Sets. In: Tsumoto, S., et al. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 78–83. Springer, Heidelberg (2004)

    Google Scholar 

  34. Zadeh, L.: Fuzzy Sets. Information and Control 8, 338–353 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  35. Ziarko, W.: Variable Precision Rough Sets Model. Journal of Computer and System Sciences 46, 39–59 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  36. Ziarko, W.: Probabilistic Rough Sets. In: Ślęzak, D., et al. (eds.) RSFDGrC 2005. LNCS (LNAI), vol. 3641, pp. 283–293. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

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Authors and Affiliations

  1. Department of Avionics and Control, Rzeszów University of Technology, ul. W. Pola 2, 35-959 Rzeszów, Poland

    Alicja Mieszkowicz-Rolka & Leszek Rolka

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  1. Alicja Mieszkowicz-Rolka
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  2. Leszek Rolka
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James F. Peters Andrzej Skowron Ivo Düntsch Jerzy Grzymała-Busse Ewa Orłowska Lech Polkowski

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Mieszkowicz-Rolka, A., Rolka, L. (2007). On Representation and Analysis of Crisp and Fuzzy Information Systems. In: Peters, J.F., Skowron, A., Düntsch, I., Grzymała-Busse, J., Orłowska, E., Polkowski, L. (eds) Transactions on Rough Sets VI. Lecture Notes in Computer Science, vol 4374. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71200-8_12

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  • DOI: https://doi.org/10.1007/978-3-540-71200-8_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-71198-8

  • Online ISBN: 978-3-540-71200-8

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