Statistical model for rough set approach to multicriteria classification

K. Dembczynski; Salvatore Greco; W. Kotlowski; R. Slowinski

doi:10.1007/978-3-540-74976-9_18

Statistical model for rough set approach to multicriteria classification

K. Dembczynski, Salvatore Greco, W. Kotlowski, R. Slowinski

Research output: Chapter in Book/Report/Conference proceeding › Chapter (peer-reviewed) › peer-review

Abstract

In order to discover interesting patterns and dependencies in data, an approach based on rough set theory can be used. In particular, Dominance-based Rough Set Approach (DRSA) has been introduced to deal with the problem of multicriteria classification. However, in real-life problems, in the presence of noise, the notions of rough approximations were found to be excessively restrictive, which led to the proposal of the Variable Consistency variant of DRSA. In this paper, we introduce a new approach to variable consistency that is based on maximum likelihood estimation. For two-class (binary) problems, it leads to the isotonic regression problem. The approach is easily generalized for the multi-class case. Finally, we show the equivalence of the variable consistency rough sets to the specific risk-minimizing decision rule in statistical decision theory.

Original language	English
Title of host publication	Knowledge discovery in databases: proceedings of the 11th european conference
Editors	J. Kok, J. Koronacki, R. Lopez de Mantaras, S. Matwin, D. Mladenic, A. Skowron
Place of Publication	Berlin
Publisher	Springer
Pages	164-175
Number of pages	12
Volume	4702
Edition	4702
ISBN (Print)	9783540749752
DOIs	https://doi.org/10.1007/978-3-540-74976-9_18
Publication status	Published - 2007

Publication series

Name	Lecture notes in computer science
Publisher	Springer
Number	4702
ISSN (Print)	0302-9743

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10.1007/978-3-540-74976-9_18

http://link.springer.com/chapter/10.1007%2F978-3-540-74976-9_18

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Dembczynski, K., Greco, S., Kotlowski, W., & Slowinski, R. (2007). Statistical model for rough set approach to multicriteria classification. In J. Kok, J. Koronacki, R. Lopez de Mantaras, S. Matwin, D. Mladenic, & A. Skowron (Eds.), Knowledge discovery in databases: proceedings of the 11th european conference (4702 ed., Vol. 4702, pp. 164-175). (Lecture notes in computer science; No. 4702). Springer. https://doi.org/10.1007/978-3-540-74976-9_18

Dembczynski, K. ; Greco, Salvatore ; Kotlowski, W. et al. / Statistical model for rough set approach to multicriteria classification. Knowledge discovery in databases: proceedings of the 11th european conference. editor / J. Kok ; J. Koronacki ; R. Lopez de Mantaras ; S. Matwin ; D. Mladenic ; A. Skowron. Vol. 4702 4702. ed. Berlin : Springer, 2007. pp. 164-175 (Lecture notes in computer science; 4702).

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abstract = "In order to discover interesting patterns and dependencies in data, an approach based on rough set theory can be used. In particular, Dominance-based Rough Set Approach (DRSA) has been introduced to deal with the problem of multicriteria classification. However, in real-life problems, in the presence of noise, the notions of rough approximations were found to be excessively restrictive, which led to the proposal of the Variable Consistency variant of DRSA. In this paper, we introduce a new approach to variable consistency that is based on maximum likelihood estimation. For two-class (binary) problems, it leads to the isotonic regression problem. The approach is easily generalized for the multi-class case. Finally, we show the equivalence of the variable consistency rough sets to the specific risk-minimizing decision rule in statistical decision theory.",

author = "K. Dembczynski and Salvatore Greco and W. Kotlowski and R. Slowinski",

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Dembczynski, K, Greco, S, Kotlowski, W & Slowinski, R 2007, Statistical model for rough set approach to multicriteria classification. in J Kok, J Koronacki, R Lopez de Mantaras, S Matwin, D Mladenic & A Skowron (eds), Knowledge discovery in databases: proceedings of the 11th european conference. 4702 edn, vol. 4702, Lecture notes in computer science, no. 4702, Springer, Berlin, pp. 164-175. https://doi.org/10.1007/978-3-540-74976-9_18

Statistical model for rough set approach to multicriteria classification. / Dembczynski, K.; Greco, Salvatore; Kotlowski, W. et al.
Knowledge discovery in databases: proceedings of the 11th european conference. ed. / J. Kok; J. Koronacki; R. Lopez de Mantaras; S. Matwin; D. Mladenic; A. Skowron. Vol. 4702 4702. ed. Berlin: Springer, 2007. p. 164-175 (Lecture notes in computer science; No. 4702).

Research output: Chapter in Book/Report/Conference proceeding › Chapter (peer-reviewed) › peer-review

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AB - In order to discover interesting patterns and dependencies in data, an approach based on rough set theory can be used. In particular, Dominance-based Rough Set Approach (DRSA) has been introduced to deal with the problem of multicriteria classification. However, in real-life problems, in the presence of noise, the notions of rough approximations were found to be excessively restrictive, which led to the proposal of the Variable Consistency variant of DRSA. In this paper, we introduce a new approach to variable consistency that is based on maximum likelihood estimation. For two-class (binary) problems, it leads to the isotonic regression problem. The approach is easily generalized for the multi-class case. Finally, we show the equivalence of the variable consistency rough sets to the specific risk-minimizing decision rule in statistical decision theory.

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BT - Knowledge discovery in databases: proceedings of the 11th european conference

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Dembczynski K, Greco S, Kotlowski W, Slowinski R. Statistical model for rough set approach to multicriteria classification. In Kok J, Koronacki J, Lopez de Mantaras R, Matwin S, Mladenic D, Skowron A, editors, Knowledge discovery in databases: proceedings of the 11th european conference. 4702 ed. Vol. 4702. Berlin: Springer. 2007. p. 164-175. (Lecture notes in computer science; 4702). doi: 10.1007/978-3-540-74976-9_18

Statistical model for rough set approach to multicriteria classification

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