Rough Set Approach with Imperfect Data Based on Dempster-Shafer Theory
Do Van Nguyen, Koichi Yamada, and Muneyuki Unehara
Department of Management and Information Systems Science, Nagaoka University of Technology, 1603-1 Kamitomioka, Nagaoka, Niigata 940-2188, Japan
Original rough set theory deals with precise and complete data, even though real applications frequently contain imperfect information. Missing values are typical imperfect data studied in rough set research. Many ideas have been proposed in the literature to solve the issue of imperfect data, but hardly a single solution is sufficient for multiple types of imperfect data containing imprecision and uncertainty. The paper models some basic relations between objects with respect to an imperfect attribute value using the Dempster-Shafer theory of evidence, and defines uncertain relations between objects with multiple imperfect attribute values by combining basic relations defined in a single attribute. It also proposes new rough set models based on these basic relations and discusses the properties of these models.
-  Z. Pawlak, “Rough Sets,” Int. J. of Computer and Information Sciences, Vol.11, pp. 341-356, 1982.
-  Z. Pawlak, “Rough Sets. Theoretical Aspects of Reasoning about Data,” Kluwer Acad. Publisher, 1991.
-  Y. Feng, W. Li, Z. Lv, and X. Ma, “Probabilistic approximation under incomplete information systems,” IFIP Int. Federation for Information Proc., Vol.228, Intelligent Information processing III, Z. Shi, K. Shimohara, and D. Feng (Eds.), Springer, Boston pp. 71-80, 2006.
-  J. W. Grzymala-Busse, “Characteristic relations for incomplete data: A generalization of the indiscernibility relation,” In: Proc. of the RSCTC 2004, Fourth Int. Conf. on Rough Sets and Current Trends in Computing, Uppsala, Sweden, pp. 244-253, 2004.
-  J. W. Grzymala-Busse and W. J. Grzymala-Busse, “Handling missing attribute values,” in The Data Mining and Knowledge Discovery Handbook, O. Maimon and L. Rokach (Eds.), Springer-Verlag, pp. 37-57, 2005.
-  J. W. Grzymala-Busse, “A Rough Set approach to Data with Missing Attribute values,” In: Proc. of the RSKT 2006, LNAI, Vol.4062, Springer-Verlag, pp. 58-67, 2006.
-  M. Kryszkiewicz, “Rough set approach to incomplete information system,” Information Sciences, Vol.112, Issues 1-4, pp. 39-49, 1998.
-  M. Kryszkiewicz, “Rules in incomplete information systems,” Information Sciences, Vol.113, Issues 3-4, pp. 271-292, 1999.
-  J. Stefanowski and A. Tsoukias, “On the extension of rough sets under incomplete information,” Lecture Notes in Artificial Intelligence, Vol.1711, pp. 73-81, 1999.
-  J. Stefanowski and A. Tsoukias, “Incomplete Information Tables and Rough Classification,” Computational Intelligence, Vol.17, pp. 545-566, 2001.
-  G. Y.Wang, “Extension of Rough Set under Incomplete Information Systems,” FUZZ-IEEE 2002, the 2002 IEEE Int. Conf. on Fuzzy Systems, pp. 1098-1103, 2002.
-  X. Yang, X. Song, and X. Hu, “Generalisation of rough set for rule induction in incomplete system,” Int. J. of Granular Computing, Rough Sets and Intelligent Systems, Vol.2, No.1/2011, pp. 37-50, 2011.
-  A. Motro, “Uncertainty management information systems: From needs to solutions,” Kluwer Acad. Publisher, Chapter 2, 1997.
-  R. Cavallo andM. Pittarelli, “The theory of probabilistic databases,” Proc. of the 13th Very Large Database, Brighton, 1987.
-  D. V. Nguyen, K. Yamada, and M. Unehara, “On Probability of Matching in Probability Based Rough Set Definitions,” IEEESMC2013, pp. 449-454, Manchester, UK, Oct. 14, 2013.
-  D. V. Nguyen, K. Yamada, and M. Unehara, “Rough Sets and Rule Induction in Imperfect Information Systems,” Int. J. of Computer Applications, Vol.89, No.5, pp. 1-8, Mar. 2014.
-  D. V. Nguyen, K. Yamada, and M. Unehara, “Knowledge reduction in incomplete decision tables using Probabilistic Similarity-Based Rough set Model,” 12th Int. Symposium on Advanced Intelligent Systems (ISIS 2011), pp. 147-150, Suwon, Korea, Sep. 29, 2011.
-  D. V. Nguyen, K. Yamada, and M. Unehara, “Rough Set Model Based on Parameterized Probabilistic Similarity Relation in Incomplete Decision Tables,” SCIS-ISIS2012, pp. 577-582, Kobe, Japan, Nov. 2012.
-  D. V. Nguyen, K. Yamada, and M. Unehara, “Extended Tolerance Relation to Define a New Rough Set Model in Incomplete Information Systems,” Advances in Fuzzy Systems, Vol.2013, Article ID 372091, Oct. 2, 2013.
-  G. Shafer, “A Mathematical Theory of Evidence,” Princeton University Press, Princeton, NJ, 1976.
-  K. Yamada, “A new combination of evidence based on compromise,” Fuzzy Sets and Systems, Vol.159, pp. 1689-1707, 2008.
-  D. Dubois and H. Prade, “Representation and combination of uncertainty with belief functions and possibility measures,” Comput. Intelligence, Vol.1, No.1, pp. 244-264,1988.
-  T. Inagaki, “Interdependence between safety-control policy and multiple-sensor schemes via Dempster-Shafer theory,” IEEE Trans. Reliability, Vol.40, No.2, pp. 182-188, 1991.
-  R. R. Yager, “On the relationships of methods of aggregation of evidence in expert systems,” Cybernet. Systems, Vol.16, pp. 1-21, 1985.
-  R. R. Yager, “On the Dempster-Shafer framework and new combination rules,” Inform. Sci., Vol.41, pp. 93-137, 1987.
-  L. Zhang, “Representation independence, and combination of evidence in the Dempster-Shafer theory,” in: R. R. Yager, M. Fedrizzi, and F. Kacprzyk (Eds.), Advances in the Dempster-Shafer Theory of Evidence, Wiley, New York, pp. 51-69, 1994.
-  G. J. Klir and B. Yuan, “Fuzzy Sets and Fuzzy Logic, Theory and Application,” Prentice Hall Inc., NJ 1995.
-  Y. Ma, J. S. Chandler, and D. C.Wilkins, “On The Decision Making Problem in Dempster-Shafer Theory,” In Proc., Int. Symposium on Artificial Intelligence, Cancun, Mexico, pp. 293-302, Dec. 7-11, 1992.
-  J.W. Grzymala-Busse and W. Rzasa, “Definability and Other Properties of Approximations for Generalized Indiscernibility Relations,” Trans. on Rough Sets XI, LNCS, Vol.5946, Springer-Verlag, pp. 14-39, 2010.
-  Y. Y. Yao, “On generalizing rough set theory, Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing,” Proc. of the 9th Int. Conf. (RSFDGrC 2003), LNAI, Vol.2639, pp. 44-51, 2003.
-  Y. Y. Yao, “Relational interpretations of neighborhood operators and rough set approximation operators,” Information Sciences, Vol.111, No.1-4, pp. 239-259, 1998.
-  Y. Y. Yao, “Rough Sets. Neighborhood Systems, and Granular Computing,” Proc. of the IEEE Canadian Conf. on Electrical and Computer Engineering, pp. 1553-1558, 1999.
-  M. Nagamachi, “KANSEI Engineering: a new ergonomics consumer-oriented technology for product development,” Int. J. Ind. Des., Vol.15, No.1, pp. 3-11, 1995.
-  M. Nagamachi, “KANSEI Engineering as a powerful consumeroriented technology for product development,” Appl. Ergonom., Vol.33, No.3, pp. 289-294, 2002.
-  J. A. Barnett, “Computational methods for a mathematical theory of evidence,” in: Proc., 7th Int. Joint Conf. Artificial Intelligence, Vanouver, BC, pp. 868-875, 1981.
-  G. Shafer and R. Logan, “Implementing Dempster’s rule for hierarchical evidence,” Artificial Intelligence, Vol.33, pp. 271-298, 1987.
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