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Reasoning about Data — A Rough Set Perspective

  • Zdzisław Pawlak
Conference paper
  • 590 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1424)

Abstract

The paper contains some considerations concerning the relationship between decision rules and inference rules from the rough set theory perspective. It is shown that decision rules can be interpreted as a generalization of the modus ponens inference rule, however there is an essential difference between these two concepts. Decision rules in the rough set approach are used to describe dependencies in data, whereas modus ponens is used in general to derive conclusions from premises.

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References

  1. 1.
    Adams, E. W.: The logic of Conditionals, An Application of Probability to Deductive Logic. D. Reidel Publishing Company, Dordrecht, Boston (1975)zbMATHGoogle Scholar
  2. 2.
    Bandler, W. Kohout, L.: Fuzzy power sets and fuzzy implication operators. Fuzzy Sets and Systems 4 (1980) 183–190CrossRefMathSciNetGoogle Scholar
  3. 3.
    Banerjee, M., Chakraborty, M.K.: Rough logics: A survay with further directions. In: E. Orłowska (ed.): Incomplete information: Rough set analysis. Physica-Verlag, Heidelberg (1997) 579–600Google Scholar
  4. 4.
    Borkowski, L. (ed.): Jan Lukasiewicz — Selected Works. North Holland Publishing Company, Amsterdam, London, Polish Scientific Publishers, Warszawa (1970)Google Scholar
  5. 5.
    Dempster, A. P.: Upper and lower probabilities induced by induced by the multiplevalued mapping. Ann. Math. Statistics 38 (1967) 325–339zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Demri, S., Orłowska, E.: Logical analysis of indiscernibility. Institute of Computer Science, Warsaw University of Technology, ICS Research Report 11/96 (1996); see also: E. Or lowska (ed.): Incomplete information: Rough set analysis. Physica-Verlag, Heidelberg (1997) 347–380Google Scholar
  7. 7.
    Gabbay, D., Guenthner, F.: Handbook of Philosophical Logic Vol.1, Elements of Classical Logic, Kluwer Academic Publishers, Dordrecht, Boston, London (1983)Google Scholar
  8. 8.
    Lukasiewicz, J.: Die logischen Grundlagen der Wahrscheinlichkeitsrechnung. Krakow (1913)Google Scholar
  9. 9.
    Magrez, P., Smets, P.: Fuzzy modus ponens: A new model suitable for applications in knowledge-based systems. Information Journal of Intelligent Systems 4 (1975) 181–200CrossRefGoogle Scholar
  10. 10.
    Orłowska, E.: Modal logics in the theory of information systems. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 30 (1984) 213–222CrossRefzbMATHGoogle Scholar
  11. 11.
    Pagliani, P.: Rough set theory and logic-algebraic structures. In: E. Orłowska (ed.): Incomplete information: Rough set analysis. Physica-Verlag, Heidelberg (1997) 109–190Google Scholar
  12. 12.
    Pawlak, Z.: Rough probability. Bull. Polish Acad., Sci. Tech. 33(9–10) (1985) 499–504zbMATHMathSciNetGoogle Scholar
  13. 13.
    Pawlak, Z.: Rough set theory and its application to data analysis. Systems and Cybernetics (to appear)Google Scholar
  14. 14.
    Pawlak, Z.: Granularity of knowledge, indiscernibility and rough sets. IEEE Conference on Evolutionary Computation (1998) 100–103Google Scholar
  15. 15.
    Pawlak, Z.: Rough Modus Ponens. IPMU’98 Conference, Paris (1998)Google Scholar
  16. 16.
    Polkowski, L., Skowron, A.: Rough Mereology. Proc. of the Symphosium on Methodologies for Intelligent Systems 869 (1994) 85–94, Charlotte, N.C., Lecture Notes in Artificial Intelligence, Springer VerlagGoogle Scholar
  17. 17.
    Polkowski, L., Skowron, A.: Rough Mereology: A New Paradigm for Approximate Reasoning. Journ. of Approximate Reasoning 15(4) (1996) 333–365zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Rasiowa, H., Marek, W.: Approximating sets with equivalence relations. Theoret. Comput. Sci. 48 (1986) 145–152zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Rasiowa, H., Skowron, A.: Rough concepts logic. In: A. Skowron (ed.), Computation Theory, Lecture Notes in Computer Science 208 (1985) 288–297Google Scholar
  20. 20.
    Rauszer, C.: A logic for indiscernibility relations. In: Proceedings of the Conference on Information Sciences and Systems, Princeton University (1986) 834–837Google Scholar
  21. 21.
    Skowron, A.: Management of uncertainty in AI: A rough set approach. In: V. Alagar, S. Belgrer and F.Q. Dong (eds.) Proc. SOFTEKS Workshop on Incompleteness and Uncertainty in Information Systems, Springer Verlag and British Computer Society (1994) 69–86Google Scholar
  22. 22.
    Trillas, E., Valverde, L.: On implication and indistinguishability in the setting of fuzzy logic. Management Decision Support Systems Using Fuzzy Sets and Possibility Theory, Verlag TÜ (1985) 198–212Google Scholar
  23. 23.
    Vakarelov, D.: A modal logic for similarity relations in Pawlak knowledge representation systems. Fundamental Informaticae 15 (1991) 61–79zbMATHMathSciNetGoogle Scholar
  24. 24.
    Wong, S.K.M., Ziarko, W.: On learning and evaluation of decision rules in the context of rough sets. Proceedings of the International Symposium on Methodologies for Intelligent Systems (1986) 308–224Google Scholar
  25. 25.
    Zadeh, L.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1 (1977) 3–28CrossRefMathSciNetGoogle Scholar
  26. 26.
    Zadeh, L.: The role of fuzzy logic in in the management of uncertainty in expert systems. Fuzzy Sets and Systems 11 (1983) 199–277zbMATHCrossRefMathSciNetGoogle Scholar
  27. 27.
    Ziarko, W., Shan, N.: KDD-R: A comprehensive system for knowledge discovery using rough sets. Proceedings of the International Workshop on Rough Sets and Soft Computing (RSSC’94) 164–173, San Jose (1994); see also: T. Y. Lin and A. M. Wildberger (eds.), Soft Computing, Simulation Councils, Inc. (1995) 298–301Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Zdzisław Pawlak
    • 1
  1. 1.Institute of Theoretical and Applied InformaticsPolish Academy of SciencesGliwicePoland

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