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Tran Thi Thanh Huyen, Le Ba Dung, Nguyen Do Van, Mai Van Dinh


Rough membership functions in covering approximation space not only give numerical characterizations of covering-based rough set approximations, but also establish the relationship between covering-based rough sets and fuzzy covering-based rough sets. In this paper, we introduce a new method to update the approximation sets with rough membership functions in covering approximation space. Firstly, we present the third types of rough membership functions and study their properties. And then, we consider the change of them while simultaneously adding and removing objects in the information system. Based on that change, we propose a method for updating the approximation sets when the objects vary over time.


Rough Sets, covering-based rough set, Rough membership function, Incomplete Information Systems, approximation sets, Incremental Learning

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. Z. Bonikowski, E. Bryniarski, U. Wybraniec-Skardowska, “Extensions and intentions in the rough set theory”, Information Sciences 107, 149–167 (1998).

. Chen, H.M., Li, T.R., Ruan, D., Lin, J.H., Hu, C.X. Hu, “A rough-set based incremental approach for updating approximations under dynamic maintenance environments”, IEEE Transactions on Knowledge and Data Engineering 25(2), 274–284 (2013).

. Deng T, Chen Y, Xu W, Dai Q, “A novel approach to fuzzy rough sets based on a fuzzy covering”, Information Sciences, 177(11):2308–2326 (2007).

. Dubois D, Prade H, “Rough fuzzy sets and fuzzy rough sets”, International Journal of General Systems, 17:191–201 (1990).

. Greco S, Matarazzo B, Słowinski R, “Parameterized rough set model using rough membership and Bayesian confirmation measures”, International Journal of Approximate Reasoning, 2008.49(2):285–300 (2008).

. Hu BQ, Wong H, “Generalized interval-valued fuzzy rough sets based on interval-valued fuzzy logical operators”, International Journal of Fuzzy Systems, 2013.15(4):381–391 (2013).

. Hu BQ, Wong H, “Generalized interval-valued fuzzy variable precision rough sets”, International Journal of Fuzzy Systems, 2014.16(4):554–565 (2014).

. Kryszkiewicz M., “Rough set approach to incomplete information systems”, Information Science, Vol. 112, pp. 39-49 (1998).

. Li T, Ma J, “Fuzzy approximation operators based on coverings”, In: International Workshop on Rough Sets, Fuzzy Sets, Data Mining, and Granular Soft Computing. Springer, pp. 55–62 (2007).

. 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”, Knowledge Based Systems 20. 485 - 494, (2007).

. G. P. Lin, J. Y. Liang, Y. H. Qian, “Multigranulation rough sets : from partition to covering”, Inform. Sci. 241, 101-118 (2013).

. C. Luo, T. R. Li and H. M. Chen, “Dynamic maintenance of approximations in setvalued ordered decision systems under the attribute generalization”, Information Sciences 257. 210 - 228, (2014).

. Do Van Nguyen, Koichi Yamada, and Muneyuki Unehara, “Rough Set Model Based on Parameterized Probabilistic Similarity Relation in Incomplete Decision Tables”, SCIS-ISIS 2012, Kobe, Japan, November 20-24, (2012).

. Do Van Nguyen, Koichi Yamada, and Muneyuki Unehara, “On Probability of Matching in Probability Based Rough Set Definitions”, 2013 IEEE International Conference on Systems, Man, and Cybernetics (2013).

. Do Van Nguyen, Koichi Yamada, and Muneyuki Unehara, “Extended Tolerance Relation to Define a New Rough Set Model in Incomplete Information Systems”, Advances in Fuzzy Systems Volume 2013, Article ID 372091, 10 pages (2013).

. Pawlak, Z., “Rough Sets”, Int. J. of Computer and Information Sciences, Vol.11, pp. 341-356 (1982).

. J.A. Pomykala, “Approximation operations in approximation space”, Bulletin Polonaise Academy of Science 35 (9–10), 653–662 (1987).

. Radzikowska A, Kerre E, “A comparative study of fuzzy rough sets”, Fuzzy Sets and Systems, 126(2):137–155 (2002).

. Radzikowska AM, Kerre EE, “Fuzzy rough sets based on residuated lattices”, In: Transactions on Rough Sets, volume 3135 of LNCS, pp. 278–296 (2004).

. Stefanowski J. and Tsouki A., “On the extension of rough sets under

incomplete information,” Lecture Notes in ArtificialIntelligence 1711, pp.73-81, (1999).

. Z. H. Shi, Z. T. Gong, “The further investigation of covering-based rough sets: uncertainty characterization, similarity measure and generalized models”, Inform. Sci. 180, 3745-3763 (2010).

. Wu W, Zhang W, “Constructive and axiomatic approaches of fuzzy approximation operators”, Information Sciences, 159(3-4), 233–254 (2004).

. Ge X, Wang P, Yun Z, “The rough membership functions on four types of covering-based rough sets and their applications”, Information Sciences, 390:1–14 (2017).

. B. Yang, B. Q. Hu, J. Qiao, “Three-way Decisions with Rough Membership Functions in Covering Approximation Space”, Fundamenta Informaticae 165, 157–191(2019).

. W. Xu and W. X. Zhang, Measuring roughness of generalized rough sets induced by a covering, Fuzzy Sets and Systems 158, 2443–2455 (2007).

. Y. Y. Yao and S. K. M. Wong, “A decision-theoretic framework for

approximating concepts”, International Journal of Man-Machine Studies.

(6), 793 – 804 (1992).

. Yao Y, Yao B, “Covering based rough set approximations”, Information Sciences,200:91–107 (2012).

. W. Zhu and F.Y Wang, “On Three Types of Covering-Based Rough Sets”, IEEE transactions on knowledge and data engineering, vol. 19, no. 8, August, 1131-1144 (2007).

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Journal of Computer Science and Cybernetics ISSN: 1813-9663

Published by Vietnam Academy of Science and Technology