A method for incremental updating three-way decision with incomplete information system
152 viewsDOI:
https://doi.org/10.54939/1859-1043.j.mst.83.2022.59-71Keywords:
Rough Sets; Incomplete Information Systems; Three-way Decisions; Incremental Learning.Abstract
In recent years, the three-way decisions theory has been developed in both theoretical and practical applications. In fact, data are often incomplete and often change over time. To solve this problem, a method of updating the three-way decisions in the dynamic incomplete information system is proposed. First, we consider the relationship between the change of conditional probabilities for the change of the three regions. Then, we consider the change of conditional probability when objects and attribute values of the object change. From that change, we propose a method for updating three-way decisions for two situations, namely, the objects vary, and the attribute values of an object vary. Finally, we give an example to illustrate this method.
References
[1]. P. Z., “Rough Sets,” International Journal of Computer and Information Sciences, vol. 11, pp. 341–356 (1981). DOI: https://doi.org/10.1007/BF01001956
[2]. Yao. Y. Y, “Probabilistic rough set approximations,” International Journal of Approximation Reasoning 49, pp. 255–271 (2008). DOI: https://doi.org/10.1016/j.ijar.2007.05.019
[3]. Yao. Y. Y, “Three-way decisions with probabilistic rough set,” Information Sciences 180, pp. 341–353 (2010). DOI: https://doi.org/10.1016/j.ins.2009.09.021
[4]. Yao. Y. Y, “Three-way decisions with probabilistic rough set,” Information Sciences 181, pp. 1080–1096, (2011). DOI: https://doi.org/10.1016/j.ins.2010.11.019
[5]. Yao. Y. Y, “An outline of a theory of three-way decisions,” in Yao, J., Yang, Y., Slowinski, R., Greco, S., Li, H., Mitra, S., Polkowski, L. (eds.) RSCTC 2012. LNCS (LNAI), vol. 7413, pp. 1–17 (2012).
[6]. T. R. Li, D. Ruan, W. Geert, J. Song and Y. Xu, “A rough sets based characteristic relation approach for dynamic attribute generalization in data mining,” KnowledgeBased Systems 20, pp. 485–494 (2007). DOI: https://doi.org/10.1016/j.knosys.2007.01.002
[7]. Chien-Chung Chart, “A rough set approach to attribute generalization in data mining,” Journal of Information Sciences 107, pp. 169–176 (1998). DOI: https://doi.org/10.1016/S0020-0255(97)10047-0
[8]. H. M. Chen, T. R. Li, D. Ruan, J. H. Lin and C. X. Hu, “Threeway decisions in dynamic decision theoretic rough sets,” in IEEE Transactions on Knowledge and Data Engineering, vol. 25, no. 2. Springer, Heidelberg, pp. 274–284 (2013). DOI: https://doi.org/10.1109/TKDE.2011.220
[9]. C. Luo, T. R. Li and H. M. Chen, “Dynamic Maintenance of Three-Way Decision Rules,” in rough set and knowledge technology, pp. 801–811 (2014). DOI: https://doi.org/10.1007/978-3-319-11740-9_73
[10]. C. Luo, T. R. Li and H. M. Chen, “Dynamic maintenance of approximations in set-valued ordered decision systems under the attribute generalization,” in Information Sciences 257, pp. 210–228 (2014). DOI: https://doi.org/10.1016/j.ins.2013.09.035
[11]. Xin Yang, Tianrui Li, Dun Liu, Hongmei Chen and C. Luo, “A unified framework of dynamic three-way probabilistic rough sets,” Information Sciences (2017). DOI: https://doi.org/10.1016/j.ins.2017.08.053
[12]. Yao. Y. Y, “Granular computing and sequential three-way decisions,” in Lingras, P., Wolski, M., Cornelis, C., Mitra, S., Wasilewski, P. (eds.) RSKT 2013, LNCS, vol. 8171, pp. 16–27 (2013).
[13]. H. Li, X. Zhou, B. Huang, and D. Liu, “Cost-sensitive threeway decision: A sequential strategy,” in Lingras, P., Wolski, M., Cornelis, C., Mitra, S., Wasilewski, P. (eds.) RSKT 2013, LNCS, vol. 8171. Springer, Heidelberg, pp. 325–337 (2013).
[14]. D. Liu, T. Li, and D. Liang, “Three-way decisions in dynamic decision theoretic rough sets,” in Lingras, P., Wolski, M., Cornelis, C., Mitra, S., Wasilewski, P. (eds.) RSKT 2013, LNCS, vol. 8171. Springer, Heidelberg, pp. 291–301 (2013). DOI: https://doi.org/10.1007/978-3-642-41299-8_28
[15]. C. Luo and T. R. Li, “Incremental three-way decisions with incomplete information,” in Rough sets and current trends in computing, pp. 128–135 (2014). DOI: https://doi.org/10.1007/978-3-319-08644-6_13
[16]. J. Xu, D. Miao, Y.Zhang and Z. Zhang, “A Three-way Decisions Model with Probabilistic Rough Sets for Stream Computing,” International Journal of Approximate Reasoning (2017).
[17]. C. Luo, T. R. Li, H. Chen and D. Liu, “Incremental approaches for updating approximations in set-valued ordered information systems,” in Knowledge-Based Systems, vol. 50, pp. 218–223 (2013). DOI: https://doi.org/10.1016/j.knosys.2013.06.013
[18]. H. M. Chen, T. R. Li, C. Luo, S. J. Horng and G. Wang, “A Rough Set-Based Method for Updating Decision Rules on Attribute Values’ Coarsening and Refining,” in IEEE Transactions on Knowledge and Data Engineering, vol. 26, no. 12, pp. 2886–2889 (2014). DOI: https://doi.org/10.1109/TKDE.2014.2320740
[19]. A.P. zeng,T. R. Li, J. Hu, H. M. Chen and C. Luo, “Dynamical updating fuzzy rough approximations for hybrid data under the variation of attribute values,” Information Sciences, pp. 1–26 (2016). DOI: https://doi.org/10.1109/ICMLC.2015.7340915
[20]. C. Luo, T. R. Li, Y.Y. Huang and H. Fujita, “Updating threeway decisions in incomplete multi-scale information systems,” Information Sciences, pp. 1–19 (2018).
[21]. K. M., “Rough set approach to incomplete information system,” Information Sciences, vol. 112 (1998). DOI: https://doi.org/10.1016/S0020-0255(98)10019-1
[22]. R. O. Duda and P. E. Hart, “Pattern Classification and Scene Analysis,” Wiley, New York (1973).
[23]. Y. Y. Yao, “Rough Sets: neighborhood systems, and granular computing,” in Proceedings of the IEEE Canadian Conference on Electrical and Computer Engineering, pp. 1553–1558 (1999).
[24]. B. Zhou, Y. Y. Yao, and J. Luo, in Farzindar, A., Keˇselj, V. (eds.) Canadian AI. LNCS (LNAI), vol. 6085 (2010).
[25]. D. Liu, Y. Y. Yao, and T. R. Li, “Three-way investment decisions with Decision theoretic rough sets,” International Journal of Computational Intelligence Systems 4, pp. 66–74 (2011). DOI: https://doi.org/10.1080/18756891.2011.9727764
[26]. H. Yu, Z. G. Liu, and G. Y. Wang, “An automatic method to determine the number of clusters using decision-theoretic rough set,” International Journal of Approximate Reasoning 55(1), pp. 101–115 (2014). DOI: https://doi.org/10.1016/j.ijar.2013.03.018
[27]. H. Tran, T. Cao, K. Yamada, and D. V. Nguyen, “Incremental updating methods with three-way decision models in incomplete information systems,” in SCISISIS2018 (2018). DOI: https://doi.org/10.1109/SCIS-ISIS.2018.00016