Abstract
We propose a new fuzzy rough set approach which, differently from most known fuzzy set extensions of rough set theory, does not use any fuzzy logical connectives (t-norm, t-conorm, fuzzy implication). As there is no rationale for a particular choice of these connectives, avoiding this choice permits to reduce the part of arbitrary in the fuzzy rough approximation. Another advantage of the new approach is that it is based on the ordinal properties of fuzzy membership degrees only. The concepts of fuzzy lower and upper approximations are thus proposed, creating a base for induction of fuzzy decision rules having syntax and semantics of gradual rules. The proposed approach to rule induction is also interesting from the viewpoint of philosophy supporting data mining and knowledge discovery, because it is concordant with the method of concomitant variations by John Stuart Mill. The decision rules are induced from lower and upper approximations defined for positive and negative relationships between credibility degrees of multiple premises, on one hand, and conclusion, on the other hand.
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References
Aragones, E., Gilboa, I., Postlewaite, A., Schmeidler, D.: Accuracy vs. simplicity: A complex trade-off. PIER working, 2–27 (2002)
Bensusan, H.: Is machine learning experimental philosophy of science? In: Aliseda, A., Pearce, D. (eds.) ECAI 2000 Workshop notes on Scientific Reasoning in Artificial Intelligence and the Philosophy of Science, pp. 9–14 (2000)
Cornish, T.A.O., Elliman, A.D.: What has Mill to say about Data Mining? In: Proc. 11th Conference for AI Applications, February 20-22, pp. 347–353. IEEE Computer Society Press, Los Alamitos (1995)
Dubois, D., Prade, H., Yager, R.: Information Engineering. J.Wiley, New York (1997)
Dubois, D., Prade, H.: Gradual inference rules in approximate reasoning. Information Sciences 61, 103–122 (1992)
Greco, S., Inuiguchi, M., Slowinski, R.: Rough Sets and Gradual Decision Rules. In: Wang, G., Liu, Q., Yao, Y., Skowron, A. (eds.) RSFDGrC 2003. LNCS (LNAI), vol. 2639, pp. 156–164. Springer, Heidelberg (2003)
Greco, S., Inuiguchi, M., Słowiński, R.: A new proposal for fuzzy rough approximations and gradual decision rule representation. In: Peters, J.F., Skowron, A., Dubois, D., Grzymała-Busse, J.W., Inuiguchi, M., Polkowski, L. (eds.) Transactions on Rough Sets II. LNCS, vol. 3135, pp. 156–164. Springer, Heidelberg (2004)
Greco, S., Matarazzo, B., Slowinski, R.: The use of rough sets and fuzzy sets in MCDM. In: Gal, T., Stewart, T., Hanne, T. (eds.) Advances in Multiple Criteria Decision Making, vol. Ch. 14, pp. 14.1-14.59. Kluwer Academic Publishers, Boston (1999)
Greco, S., Matarazzo, B., Slowinski, R.: Rough sets theory for multicriteria decision analysis. Europena Journal of Operational Research 129(1), 1–47 (2001)
Greco, S., Matarazzo, B., Slowinski, R.: Decision rule approach. In: Figueira, J., Greco, S., Ehrgott, M. (eds.) Multiple Criteria Decision Analysis, State of the art Surveys,  Ch. 13, pp. 507–561. Springer, Heidelberg (2005)
Greco, S., Pawlak, Z., Slowinski, R.: Can Bayesian confirmation measures be useful for rough set decision rules? Engineering Applications of Artificial Intelligence 17, 345–361 (2004)
Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer Academic Publishers, Dordrecht (2000)
Marchant, T.: The measurement of membership by comparisons. Fuzzy Sets and Systems 148, 157–177 (2004)
Mill, J.S.: A System of Logic, Ratiocinative and Inductive: Being a connected View of the Principles of Evidence and the Methods of Scientific Investigation. In: Robson, J.M. (ed.) Collected Works. Books l-m, vol. VII. University of Toronto Press, RKP (1843/1973)
Nakamura, A., Gao, J.M.: A logic for fuzzy data analysis. Fuzzy Sets and Systems 39, 127–132 (1991)
Pawlak, Z.: Rough Sets. International Journal of Computer and Information Sciences 11, 341–356 (1982)
Pawlak, Z.: Rough Sets. Kluwer, Dordrecht (1991)
Williamson, J.: A dynamic interaction between machine learning and the philosophy of science. Minds and Machine 14(4), 539–549 (2004)
Wittgenstein, L.: Tractatus Logico-Philosophicus. Routledge and Kegan Paul, London (1922) (fifth impression 1951)
Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–353 (1965)
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Greco, S., Inuiguchi, M., Slowinski, R. (2006). Fuzzy Rough Sets and Multiple-Premise Gradual Decision Rules. In: Di Gesú, V., Masulli, F., Petrosino, A. (eds) Fuzzy Logic and Applications. WILF 2003. Lecture Notes in Computer Science(), vol 2955. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10983652_20
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DOI: https://doi.org/10.1007/10983652_20
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