Abstract
This paper investigates decision-theoretic rough set approach in the frameworks of multi-covering approximation space. We mainly discuss optimistic multigranulation decision-theoretic rough sets by employing maximal descriptors of elements. First, we present the definitions of covering-based optimistic multigranulation decision-theoretic rough sets on the basis of Bayesian decision procedure. Then, we disclose some important and interesting properties of the model. Finally, we investigate the relationships between the proposed model and other related rough set models.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Yao, Y.Y., Wong, S.K.M.: A decision theoretic framework for approximating concepts. Int. J. Man-Mach. Stud. 37, 793–809 (1992)
Herbert, J.P., Yao, J.T.: Game-theoretic rough sets. Fundam. Inform. 108(3–4), 267–286 (2011)
Liu, D., Li, T.R., Li, H.X.: A multiple-category classification approach with decision-theoretic rough sets. Fundam. Inform. 115(2–3), 173–188 (2012)
Yu, H., Liu, Z.G., Wang, G.Y.: An automatic method to determine the number of clusters using decision-theoretic rough set. Int. J. Approx. Reason. 55(1), 101–115 (2014)
Li, T.J., Yang, X.P.: An axiomatic characterization of probabilistic rough sets. Int. J. Approx. Reason. 55(1), 130–141 (2014)
Jia, X.Y., Tang, Z.M., Liao, W.H., Shang, L.: On an optimization representation of decision-theoretic rough set model. Int. J. Approx. Reason. 55(1), 156–166 (2014)
Yao, Y.Y.: Three-way decisions with probabilistic rough sets. Inf. Sci. 180, 341–353 (2010)
Yao, Y.: An outline of a theory of three-way decisions. In: Yao, J.T., Yang, Y., Słowiński, R., Greco, S., Li, H., Mitra, S., Polkowski, L. (eds.) RSCTC 2012. LNCS, vol. 7413, pp. 1–17. Springer, Heidelberg (2012). doi:10.1007/978-3-642-32115-3_1
Zhou, B., Yao, Y.Y., Luo, J.G.: A three-way decision approach to email spam filtering. In: Farzindar, A., Keselj, V. (eds.) Canadian AI 2010, LNAI 6085, pp. 28–39. Springer, Berlin (2010)
Li, H.X., Zhang, L.B., Huang, B., Zhou, X.Z.: Sequential three-way decision and granulation for cost-sensitive face recognition. Knowl.-Based Syst. 91, 241–251 (2016)
Zhang, H.R., Min, F.: Three-way recommender systems based on random forests. Knowl.-Based Syst. 91, 275–286 (2016)
Qian, Y.H., Zhang, H., Sang, Y.L., Liang, J.L.: Multigranulation decision-theoretic rough sets. Int. J. Approx. Reason. 55(1), 225–237 (2014)
Qian, Y.H., Liang, X.Y., Lin, G.P., et al.: Local multigranulation decision-theoretic rough sets. Int. J. Approx. Reason. 82, 119–137 (2017)
Liu, C., Wang, M.: Optimistic decision-theoretic rough sets in multi-covering space. In: Flores, V., Gomide, F., Janusz, A., Meneses, C., Miao, D., Peters, G., Ślȩzak, D., Wang, G., Weber, R., Yao, Y. (eds.) IJCRS 2016. LNCS, vol. 9920, pp. 282–293. Springer, Cham (2016). doi:10.1007/978-3-319-47160-0_26
Yao, Y.Y., Yao, B.: Covering based rough set approximations. Inf. Sci. 200, 91–107 (2012)
Zakowski, W.: Approximations in the space \((U,\Pi )\). Demonstr. Math. 16, 761–769 (1983)
Liu, C.H.: Covering-based multi-granulation rough set model based on maximal description of elements. Comput. Sci. 40(12), 64–67 (2013). (In Chinese)
Liu, C.H., Cai, K.C.: Multi-granulation covering rough sets based on the union of minimal descriptions of elements. CAAI Trans. Intell. Syst. 11(4), 534–538 (2016). (in Chinese)
Zhu, W., Wang, F.Y.: On three types of covering rough sets. IEEE Trans. Knowl. Data Eng. 19, 1131–1144 (2007)
Acknowledgements
This work was supported by the China National Natural Science Foundation of Science Foundation under Grant Nos.: 61663002, 61403329, 61305052 and Jiangxi Province Natural Science Foundation of China under Grant No.: 20171BAB202034.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Liu, C., Wang, M., Zhang, N. (2017). Covering-Based Optimistic Multigranulation Decision-Theoretic Rough Sets Based on Maximal Descriptors. In: Polkowski, L., et al. Rough Sets. IJCRS 2017. Lecture Notes in Computer Science(), vol 10314. Springer, Cham. https://doi.org/10.1007/978-3-319-60840-2_17
Download citation
DOI: https://doi.org/10.1007/978-3-319-60840-2_17
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-60839-6
Online ISBN: 978-3-319-60840-2
eBook Packages: Computer ScienceComputer Science (R0)