Abstract
Attribute reduction is one of the hottest topics in rough set data analysis. This paper extends the concept of a boundary region to a relation system and studies the boundary region reduction for a given relation system and a fixed set. We present the discernibility matrix and obtain the judgment theorem of such a type of reduction. The discernibility matrix based boundary reduction algorithm for a relation system is established.
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References
Dai, J., Wang, W., Tian, H., Liu, L.: Attribute selection based on a new conditional entropy for incomplete decision systems. Knowl. Based Syst. 39, 207–213 (2013)
Jia, X., Shang, L., Zhou, B., Yao, Y.: Generalized attribute reduct in rough set theory. Knowl. Based Syst. 91, 204–218 (2016)
Liu, G., Li, L., Yang, J., Feng, Y., Zhu, K.: Attribute reduction approaches for general relation decision systems. Pattern Recogn. Lett. 65, 81–87 (2015)
Liu, G., Hua, Z., Zou, J.: A unified reduction algorithm based on invariant matrices for decision tables. Knowl. Based Syst. 109, 84–89 (2016)
Liu, G., Hua, Z., Chen, Z.: A general reduction algorithm for relation decision systems and its applications. Knowl. Based Syst. 119, 87–93 (2017)
Liu, G., Hua, Z., Zou, J.: Local attribute reductions for decision tables. Inf. Sci. 422, 204–217 (2018)
Liu, G., Hua, Z.: Partial attribute reduction approaches to relation systems and their applications. Knowl. Based Syst. 139, 101–107 (2018)
Ma, X., Wang, G., Yu, H., Li, T.: Decision region distribution preservation reduction in decision-theoretic rough set model. Inf. Sci. 278, 614–640 (2014)
Ma, X., Yao, Y.: Three-way decision perspectives on class-specific attribute reducts. Inf. Sci. 450, 227–245 (2018)
Mi, J.S., Wu, W.Z., Zhang, W.X.: Approaches to knowledge reduction based on variable precision rough set model. Inf. Sci. 159, 255–272 (2004)
Mieszkowicz-Rolka, A., Rolka, L.: Variable precision rough rets in analysis of inconsistent decision tables. In: Rutkowski, L., Kacprzyk, J. (eds.) Advances in Soft Computing. Physica-Verlag, Heidelberg (2003)
Mieszkowicz-Rolka, A., Rolka, L.: Variable precision fuzzy rough sets. In: Peters, J.F., Skowron, A., Grzymała-Busse, J.W., Kostek, B., Świniarski, R.W., Szczuka, M.S. (eds.) Transactions on Rough Sets I. LNCS, vol. 3100, pp. 144–160. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-27794-1_6
Pawlak, Z.: Rough sets. Int. J. Comput. Inf. Sci. 11, 341–356 (1982)
Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning About Data. Kluwer Academic Publishers, Boston (1991)
Skowron, A., Rauszer, C.: The discernibility matrices and functions in information systems. In: Slowinski, R. (ed.) Intelligent Decision Support-Handbook of Applications and Advances of the Rough Set Theory, pp. 331–362, Springer, Dordrecht (1992)
Skowron, A.: Boolean reasoning for decision rules generation. In: Komorowski, J., Raś, Z.W. (eds.) ISMIS 1993. LNCS, vol. 689, pp. 295–305. Springer, Heidelberg (1993). https://doi.org/10.1007/3-540-56804-2_28
Yao, Y.: Constructive and algebraic methods of theory of rough Sets. Inf. Sci. 109, 21–47 (1998)
Ziarko, W.: Variable precision rough set model. J. Comput. Syst. Sci. 46, 39–59 (1993)
Zhang, H.Y., Leung, Y., Zhou, L.: Variable-precision-dominance-based rough set approach to interval-valued information systems. Inf. Sci. 244, 75–91 (2013)
Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant No. 61272031) and supported by Science Foundation of Beijing Language and Culture University (The Fundamental Research Funds for the Central Universities)(Grant No. 18YJ030003).
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Liu, G., Liu, J. (2018). Boundary Region Reduction for Relation Systems. In: Nguyen, H., Ha, QT., Li, T., Przybyła-Kasperek, M. (eds) Rough Sets. IJCRS 2018. Lecture Notes in Computer Science(), vol 11103. Springer, Cham. https://doi.org/10.1007/978-3-319-99368-3_32
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DOI: https://doi.org/10.1007/978-3-319-99368-3_32
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