Abstract
The concept of valued tolerance is introduced as an extension of the usual concept of indiscernibility (which is a crisp equivalence relation) in rough sets theory. Some specific properties of the approach are discussed. Further on the problem of inducing rules is addressed. Properties of a “credibility degree” associated to each rule are analysed and its use in classification problems is discussed.
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Dubois D., Prade H.: Rough Fuzzy Sets and Fuzzy Rough Sets. International Journal of General Systems, 17, (1990), 191–209.
Greco S., Matarazzo B. Slowinski R.: Fuzzy similarity relation as a basis for rough approximations. In Polkowski L., Skowron A. (eds.), Proc. of the RSCTC-98, Springer Verlag, Berlin, LNAI 1424, (1998), 283–289.
Greco S., Matarazzo B. Slowinski R.: Rough set processing of vague information using fuzzy similarity relations. In Calude C.S., Paun G. (eds), Finite vs infinite: contributions to an eternal dilemma, Springer Verlag, Berlin, (2000), 149–173.
Grzymala-Busse J.W.: On the unknown attribute values in learning from examples. Proc. of Int. Symp. on Methodologies for Intelligent Systems, (1991), 368–377.
Kitainik L.: Fuzzy Decision Procedures with Binary Relations, Kluwer Academic, Dordrecht, (1993).
Kryszkiewicz M.: Properties of incomplete information systems in the framework of rough sets. In Polkowski L., Skowron A. (eds.), Rough Sets in Data Mining and Knowledge Discovery, Physica-Verlag, Heidelberg, (1998), 422–450.
Luce R.D.: Semiorders and a theory of utility discrimination, Econometrica, 24, (1956), 178–191.
Skowron A., Stepaniuk J.: Tolerance approximation spaces, Fundamenta Informaticae, 27, (1996), 245–253.
Slowiński R., Vanderpooten D.: Similarity relation as a basis for rough approximations, In Wang P. (ed.), Advances in Machine Intelligence and Soft Computing, vol. IV., Duke University Press, (1997), 17–33.
Stefanowski J., Tsoukiàs A.: On the extension of rough sets under incomplete information, in N. Zhong, A. Skowron, S. Ohsuga, (eds.), New Directions in Rough Sets, Data Mining and Granular-Soft Computing, Springer Verlag, LNAI 1711, Berlin, (1999), 73–81.
Tsoukiàs A., Vincke Ph.: A characterization of PQI interval orders, to appear in Discrete Applied Mathematics, (2000).
Yao Y.: Combination of rough sets andfuzzy sets based on á-level sets. In Lin T.Y., Cercone N. (eds.), Rough sets and data mining, Kluwer Academic, Dordrecht, (1996), 301–321.
Yao Y., Wang T.: On rough relations: an alternative fromulation. In N. Zhong, A. Skowron, S. Ohsuga, (eds.), New Directions in Rough Sets, Data Mining and Granular-Soft Computing, Springer Verlag, LNAI 1711, Berlin, (1999), 82–90.
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Stefanowski, J., Tsoukiàs, A. (2001). Valued Tolerance and Decision Rules. In: Ziarko, W., Yao, Y. (eds) Rough Sets and Current Trends in Computing. RSCTC 2000. Lecture Notes in Computer Science(), vol 2005. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45554-X_25
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DOI: https://doi.org/10.1007/3-540-45554-X_25
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