Attribute Reduction in Stochastic Information Systems Based on α-Dominance
Year 2017,
Volume: 10 Issue: 2, 211 - 219, 28.04.2017
Emel Kızılkaya Aydoğan
,
Mihrimah Özmen
Abstract
Rough set has been commonly taken part in literature
to examine inadequate and incomplete
information systems. The efficiency of rough set with stochastic data observed
for developing convenience and scalability. In this study, we use a ranking
approach for attribute reduction in stochastic information systems and
generalized this via presenting a dominance relation. We obtained the rough set approach of
attribute reduction in stochastic information systems by establishing the
dominance degrees. Furthermore, attribute reduction methods are studied by
considering discernibility matrix and this approach is applied to explanatory
examples to demonstrate its validity. Also this research proposes many research
fields and new application areas show a tendency to concerning rough set
approach to stochastic information systems.
References
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[2]. Skowron, A., & Pawlak, Z. (2007). Rough sets: Some extensions. Information Sciences, 177(1), 28-40.
[3]. Pawlak, Z. (1991). Rough sets: theoretical aspects of reasoning about data, system theory, Knowledge Engineering and Problem Solving, vol. 9.
[4]. Hu, Q., Yu, D., Liu, J., & Wu, C. (2008). Neighborhood rough set based heterogeneous feature subset selection. Information sciences, 178(18), 3577-3594.
[5]. Li, T., Ruan, D., Geert, W., Song, J., & Xu, Y. (2007). A rough sets based characteristic relation approach for dynamic attribute generalization in data mining. Knowledge-Based Systems, 20(5), 485-494.
[6]. Qian, Y., Liang, J., Pedrycz, W., & Dang, C. (2010). Positive approximation: an accelerator for attribute reduction in rough set theory. Artificial Intelligence, 174(9), 597-618.
[7]. Zhang, J., Li, T., Ruan, D., Gao, Z., & Zhao, C. (2012). A parallel method for computing rough set approximations. Information Sciences, 194, 209-223.
[8]. Zhang, J., Li, T., Ruan, D., & Liu, D. (2012). Neighborhood rough sets for dynamic data mining. International Journal of Intelligent Systems, 27(4), 317-342.
[9]. Guan, J. W., & Bell, D. A. (1998). Rough computational methods for information systems. Artificial intelligence, 105(1), 77-103.
[10]. Qian, Y., Liang, J., & Dang, C. (2008). Converse approximation and rule extraction from decision tables in rough set theory. Computers & Mathematics with Applications, 55(8), 1754-1765.
[11]. Greco, S., Matarazzo, B., & Slowinski, R. (1998, June). A new rough set approach to multicriteria and multiattribute classification. In Rough sets and current trends in computing (pp. 60-67). Springer Berlin Heidelberg.
[12]. Greco, S., Matarazzo, B., & Slowinski, R. (2001). Rough sets theory for multicriteria decision analysis. European journal of operational research, 129(1), 1-47.
[13]. Greco, S., Matarazzo, B., & Slowinski, R. (2002). Rough sets methodology for sorting problems in presence of multiple attributes and criteria. European journal of operational research, 138(2), 247-259.
[14]. Greco, S., Matarazzo, B., Slowinski, R., & Stefanowski, J. (2000, October). An algorithm for induction of decision rules consistent with the dominance principle. In Rough sets and current trends in computing (pp. 304-313). Springer Berlin Heidelberg.
[15]. Dembczyński, K., Pindur, R., & Susmaga, R. (2003). Generation of exhaustive set of rules within dominance-based rough set approach. Electronic Notes in Theoretical Computer Science, 82(4), 96-107.
[16]. Dembczyński, K., Pindur, R., & Susmaga, R. (2003). Generation of exhaustive set of rules within dominance-based rough set approach. Electronic Notes in Theoretical Computer Science, 82(4), 96-107.
[17]. Sai, Y., Yao, Y. Y., & Zhong, N. (2001). Data analysis and mining in ordered information tables. In Data Mining, 2001. ICDM 2001, Proceedings IEEE International Conference on (pp. 497-504). IEEE.
[18]. Kotłowski, W., Dembczyński, K., Greco, S., & Słowiński, R. (2008). Stochastic dominance-based rough set model for ordinal classification. Information Sciences, 178(21), 4019-4037.
[19]. J. Martel, K. Zaras, Dominance stochastique en analyse multicritére face au risque, Cahier No. 100. Laboratoire d’Analyseet Modélisation de Systèmes pour l’Aide à la Décision. Université Paris-Dauphine, Paris, 1990.
[20]. J. Martel, S.H. Azondékon, K. Zaras, Preference relations in multicriterion analysis under risk, Belgian Journal of Operations Research, Statistics and Computer Science 31 (1992) 55–83.
[21]. Nowak, M. (2004). Preference and veto thresholds in multicriteria analysis based on stochastic dominance. European Journal of Operational Research, 158(2), 339-350.
[22]. Nowak, M. (2006). INSDECM—an interactive procedure for stochastic multicriteria decision problems. European Journal of Operational Research, 175(3), 1413-1430.
[23]. Nowak, M. (2007). Aspiration level approach in stochastic MCDM problems. European Journal of Operational Research, 177(3), 1626-1640.
[24]. Zaras, K., & Martel, J. M. (1994). Multiattribute analysis based on stochastic dominance (pp. 225-248). Springer Netherlands.
[25]. Zaras, K. (2001). Rough approximation of a preference relation by a multi-attribute stochastic dominance for determinist and stochastic evaluation problems. European Journal of Operational Research, 130(2), 305-314.
[26]. Zaras, K. (2004). Rough approximation of a preference relation by a multi-attribute dominance for deterministic, stochastic and fuzzy decision problems. European Journal of Operational Research, 159(1), 196-206.
[27]. Zawisza, M., & Trzpiot, G. (2002). Multicriteria Analysis Based On Stochastic and Probabilistic Dominance in Measuring Quality of Life. In Multiple Objective and Goal Programming (pp. 412-423). Physica-Verlag HD.
[28]. Zhang, Y., Fan, Z. P., & Liu, Y. (2010). A method based on stochastic dominance degrees for stochastic multiple criteria decision making. Computers & Industrial Engineering, 58(4), 544-552.
[29]. Lin, G., Qian, Y., & Li, J. (2012). NMGRS: Neighborhood-based multigranulation rough sets. International Journal of Approximate Reasoning, 53(7), 1080-1093.
[30]. Qian, Y., Zhang, H., Sang, Y., & Liang, J. (2014). Multigranulation decision-theoretic rough sets. International Journal of Approximate Reasoning, 55(1), 225-237.
[31]. Qian, Y., Li, S., Liang, J., Shi, Z., & Wang, F. (2014). Pessimistic rough set based decisions: a multigranulation fusion strategy. Information Sciences, 264, 196-210.
[32]. Xu, W., Sun, W., Zhang, X., & Zhang, W. (2012). Multiple granulation rough set approach to ordered information systems. International Journal of General Systems, 41(5), 475-501.
[33]. Yang, X., Qi, Y., Song, X., & Yang, J. (2013). Test cost sensitive multigranulation rough set: model and minimal cost selection. Information Sciences, 250, 184-199.
[34]. Yang, X., Song, X., She, Y., & Yang, J. (2013). Hierarchy on multigranulation structures: a knowledge distance approach. International Journal of General Systems, 42(7), 754-773.
[35]. Liu, Y., Fan, Z. P., & Zhang, Y. (2011). A method for stochastic multiple criteria decision making based on dominance degrees. Information Sciences, 181(19), 4139-4153.
[36]. Graves, S. B., & Ringuest, J. L. (2009). Probabilistic dominance criteria for comparing uncertain alternatives: A tutorial. Omega, 37(2), 346-357.
[37]. Zhang, W. X., & Qiu, G. F. (2005). Uncertain decision making based on rough sets. Publishing of Tsinghua University, Beijing.
[38]. D. Bertsekas, J. Tsitsiklis, Introduction to Probability, Athena Scientific, 2002.
[39]. W. Feller, An Introduction to Probability Theory and Its applications, Wiley, New York, 1971.
[40]. Fouss, F., Achbany, Y., & Saerens, M. (2010). A probabilistic reputation model based on transaction ratings. Information Sciences, 180(11), 2095-2123.
[41]. Lahdelma, R., Makkonen, S., & Salminen, P. (2006). Multivariate Gaussian criteria in SMAA. European Journal of Operational Research, 170(3), 957-970.
[42]. Yager, R. R., Detyniecki, M., & Bouchon-Meunier, B. (2001). A context-dependent method for ordering fuzzy numbers using probabilities. Information Sciences, 138(1), 237-255.
[43]. Qian, Y., Liang, J., & Dang, C. (2008). Interval ordered information systems. Computers & Mathematics with Applications, 56(8), 1994-2009.
[44]. Yang, X., Qi, Y., Yu, D. J., Yu, H., & Yang, J. (2015). α-Dominance relation and rough sets in interval-valued information systems. Information Sciences, 294, 334-347.
[45]. Shao, M. W., & Zhang, W. X. (2005). Dominance relation and rules in an incomplete ordered information system. International journal of intelligent systems, 20(1), 13-27.
[46]. X.B. Yang, J.Y. Yang, C. Wu, D.J. Yu, Dominance-based rough set approach and knowledge reductions in incomplete ordered information system, Inform. Sci. 178 (2008) 1219–1234.
Year 2017,
Volume: 10 Issue: 2, 211 - 219, 28.04.2017
Emel Kızılkaya Aydoğan
,
Mihrimah Özmen
References
- [1]. Pawlak, Z. (1982). Rough sets. International Journal of Computer & Information Sciences, 11(5), 341-356.
[2]. Skowron, A., & Pawlak, Z. (2007). Rough sets: Some extensions. Information Sciences, 177(1), 28-40.
[3]. Pawlak, Z. (1991). Rough sets: theoretical aspects of reasoning about data, system theory, Knowledge Engineering and Problem Solving, vol. 9.
[4]. Hu, Q., Yu, D., Liu, J., & Wu, C. (2008). Neighborhood rough set based heterogeneous feature subset selection. Information sciences, 178(18), 3577-3594.
[5]. Li, T., Ruan, D., Geert, W., Song, J., & Xu, Y. (2007). A rough sets based characteristic relation approach for dynamic attribute generalization in data mining. Knowledge-Based Systems, 20(5), 485-494.
[6]. Qian, Y., Liang, J., Pedrycz, W., & Dang, C. (2010). Positive approximation: an accelerator for attribute reduction in rough set theory. Artificial Intelligence, 174(9), 597-618.
[7]. Zhang, J., Li, T., Ruan, D., Gao, Z., & Zhao, C. (2012). A parallel method for computing rough set approximations. Information Sciences, 194, 209-223.
[8]. Zhang, J., Li, T., Ruan, D., & Liu, D. (2012). Neighborhood rough sets for dynamic data mining. International Journal of Intelligent Systems, 27(4), 317-342.
[9]. Guan, J. W., & Bell, D. A. (1998). Rough computational methods for information systems. Artificial intelligence, 105(1), 77-103.
[10]. Qian, Y., Liang, J., & Dang, C. (2008). Converse approximation and rule extraction from decision tables in rough set theory. Computers & Mathematics with Applications, 55(8), 1754-1765.
[11]. Greco, S., Matarazzo, B., & Slowinski, R. (1998, June). A new rough set approach to multicriteria and multiattribute classification. In Rough sets and current trends in computing (pp. 60-67). Springer Berlin Heidelberg.
[12]. Greco, S., Matarazzo, B., & Slowinski, R. (2001). Rough sets theory for multicriteria decision analysis. European journal of operational research, 129(1), 1-47.
[13]. Greco, S., Matarazzo, B., & Slowinski, R. (2002). Rough sets methodology for sorting problems in presence of multiple attributes and criteria. European journal of operational research, 138(2), 247-259.
[14]. Greco, S., Matarazzo, B., Slowinski, R., & Stefanowski, J. (2000, October). An algorithm for induction of decision rules consistent with the dominance principle. In Rough sets and current trends in computing (pp. 304-313). Springer Berlin Heidelberg.
[15]. Dembczyński, K., Pindur, R., & Susmaga, R. (2003). Generation of exhaustive set of rules within dominance-based rough set approach. Electronic Notes in Theoretical Computer Science, 82(4), 96-107.
[16]. Dembczyński, K., Pindur, R., & Susmaga, R. (2003). Generation of exhaustive set of rules within dominance-based rough set approach. Electronic Notes in Theoretical Computer Science, 82(4), 96-107.
[17]. Sai, Y., Yao, Y. Y., & Zhong, N. (2001). Data analysis and mining in ordered information tables. In Data Mining, 2001. ICDM 2001, Proceedings IEEE International Conference on (pp. 497-504). IEEE.
[18]. Kotłowski, W., Dembczyński, K., Greco, S., & Słowiński, R. (2008). Stochastic dominance-based rough set model for ordinal classification. Information Sciences, 178(21), 4019-4037.
[19]. J. Martel, K. Zaras, Dominance stochastique en analyse multicritére face au risque, Cahier No. 100. Laboratoire d’Analyseet Modélisation de Systèmes pour l’Aide à la Décision. Université Paris-Dauphine, Paris, 1990.
[20]. J. Martel, S.H. Azondékon, K. Zaras, Preference relations in multicriterion analysis under risk, Belgian Journal of Operations Research, Statistics and Computer Science 31 (1992) 55–83.
[21]. Nowak, M. (2004). Preference and veto thresholds in multicriteria analysis based on stochastic dominance. European Journal of Operational Research, 158(2), 339-350.
[22]. Nowak, M. (2006). INSDECM—an interactive procedure for stochastic multicriteria decision problems. European Journal of Operational Research, 175(3), 1413-1430.
[23]. Nowak, M. (2007). Aspiration level approach in stochastic MCDM problems. European Journal of Operational Research, 177(3), 1626-1640.
[24]. Zaras, K., & Martel, J. M. (1994). Multiattribute analysis based on stochastic dominance (pp. 225-248). Springer Netherlands.
[25]. Zaras, K. (2001). Rough approximation of a preference relation by a multi-attribute stochastic dominance for determinist and stochastic evaluation problems. European Journal of Operational Research, 130(2), 305-314.
[26]. Zaras, K. (2004). Rough approximation of a preference relation by a multi-attribute dominance for deterministic, stochastic and fuzzy decision problems. European Journal of Operational Research, 159(1), 196-206.
[27]. Zawisza, M., & Trzpiot, G. (2002). Multicriteria Analysis Based On Stochastic and Probabilistic Dominance in Measuring Quality of Life. In Multiple Objective and Goal Programming (pp. 412-423). Physica-Verlag HD.
[28]. Zhang, Y., Fan, Z. P., & Liu, Y. (2010). A method based on stochastic dominance degrees for stochastic multiple criteria decision making. Computers & Industrial Engineering, 58(4), 544-552.
[29]. Lin, G., Qian, Y., & Li, J. (2012). NMGRS: Neighborhood-based multigranulation rough sets. International Journal of Approximate Reasoning, 53(7), 1080-1093.
[30]. Qian, Y., Zhang, H., Sang, Y., & Liang, J. (2014). Multigranulation decision-theoretic rough sets. International Journal of Approximate Reasoning, 55(1), 225-237.
[31]. Qian, Y., Li, S., Liang, J., Shi, Z., & Wang, F. (2014). Pessimistic rough set based decisions: a multigranulation fusion strategy. Information Sciences, 264, 196-210.
[32]. Xu, W., Sun, W., Zhang, X., & Zhang, W. (2012). Multiple granulation rough set approach to ordered information systems. International Journal of General Systems, 41(5), 475-501.
[33]. Yang, X., Qi, Y., Song, X., & Yang, J. (2013). Test cost sensitive multigranulation rough set: model and minimal cost selection. Information Sciences, 250, 184-199.
[34]. Yang, X., Song, X., She, Y., & Yang, J. (2013). Hierarchy on multigranulation structures: a knowledge distance approach. International Journal of General Systems, 42(7), 754-773.
[35]. Liu, Y., Fan, Z. P., & Zhang, Y. (2011). A method for stochastic multiple criteria decision making based on dominance degrees. Information Sciences, 181(19), 4139-4153.
[36]. Graves, S. B., & Ringuest, J. L. (2009). Probabilistic dominance criteria for comparing uncertain alternatives: A tutorial. Omega, 37(2), 346-357.
[37]. Zhang, W. X., & Qiu, G. F. (2005). Uncertain decision making based on rough sets. Publishing of Tsinghua University, Beijing.
[38]. D. Bertsekas, J. Tsitsiklis, Introduction to Probability, Athena Scientific, 2002.
[39]. W. Feller, An Introduction to Probability Theory and Its applications, Wiley, New York, 1971.
[40]. Fouss, F., Achbany, Y., & Saerens, M. (2010). A probabilistic reputation model based on transaction ratings. Information Sciences, 180(11), 2095-2123.
[41]. Lahdelma, R., Makkonen, S., & Salminen, P. (2006). Multivariate Gaussian criteria in SMAA. European Journal of Operational Research, 170(3), 957-970.
[42]. Yager, R. R., Detyniecki, M., & Bouchon-Meunier, B. (2001). A context-dependent method for ordering fuzzy numbers using probabilities. Information Sciences, 138(1), 237-255.
[43]. Qian, Y., Liang, J., & Dang, C. (2008). Interval ordered information systems. Computers & Mathematics with Applications, 56(8), 1994-2009.
[44]. Yang, X., Qi, Y., Yu, D. J., Yu, H., & Yang, J. (2015). α-Dominance relation and rough sets in interval-valued information systems. Information Sciences, 294, 334-347.
[45]. Shao, M. W., & Zhang, W. X. (2005). Dominance relation and rules in an incomplete ordered information system. International journal of intelligent systems, 20(1), 13-27.
[46]. X.B. Yang, J.Y. Yang, C. Wu, D.J. Yu, Dominance-based rough set approach and knowledge reductions in incomplete ordered information system, Inform. Sci. 178 (2008) 1219–1234.