Abstract
In this paper, we investigate the approximation problem of generalized rough set model. In generalized rough sets, the binary relation on one universe is always unknown and needed to be induced by the other already-known relation. In order to evaluate the induced binary relation, we propose a pair of generalized approximations called generalized lower and upper approximations by which the induced binary relation and the already-known binary relation can be connected. We also assert that the pair of generalized approximations are related to the definitions of approximations of classical rough sets. Their algebraic properties and topology structures are first studied. More important, we both give some comparisons of the relations in the same generalized rough set model and the approximations among different generalized rough set models. In the end, some applications of the proposed approximations in covering based rough sets are presented.
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References
Pawlak Z (1982) Rough sets. Int J Comput Inf Sci 11:341–356
Pawlak Z (1991) Rough sets: theoretical aspects of reasoning about data. Kluwer Academic Publishers, Boston
Liu GL (2013) The relationship among different covering approximations. Inf Sci 250:178–183
Gp L, Jy L, Yh Q (2014) Topological approach to multigranulation rough sets. Int J Mach Learn Cybern 5:233–243
Liu NKJ, Hu YX, He YL (2014) A set covering based approach to find the reduct of variable precision rough set. Inf Sci 275:83–100
Zhao SY, Wang XZ, Chen DG, Tsang ECC (2013) Nested structure in parameterized rough reduction. Inf Sci 248:130–150
Yang HL, Li SG, Wang SY, Wang J (2012) Bipolar fuzzy rough set model on two different universes and its application. Knowl Based Syst 35:94–101
Wang XZ, Tsang ECC, Zhao SY, Chen DG, Yeung SD (2007) Learning fuzzy rules from fuzzy samples based on rough set techniques. Inf Sci 177:4493–4514
Wang XZ, Zhai JH, Lu SX (2008) Induction of multiple fuzzy decision trees based on rough set technique. Inf Sci 178(16):3188–3202
Pei DW (2005) A generalized model of fuzzy rough sets. Int J Gen Syst 34:603–613
Wu WZ, Mi JS, Zhang WX (2003) Generalized fuzzy rough sets. Inf Sci 15:263–282
Qian YH, Li SY, Liang JY, Shi ZZ, Wang F (2014) Pessimistic rough set based decisions: a multigranulation fusion strategy. Inf Sci 264:196–210
Qian YH, Liang JY, Zhang X, Dang CY (2007) Rough set approach under dynamic granulation in incomplete information systems. Lect Notes Comput Sci 4827:1–8
Qian YH, Liang JY, Dang CY (2008) Converse approximation and rule extraction from decision tables in rough set theory. Comput Math Appl 55:1754–1765
Qian YH, Liang JY, Yao YY, Dang CY (2010) MGRS: a multi-granulation rough set. Inf Sci 180:949–970
Qian YH, Zhang H, Sang YL, Liang JY (2014) Multigranulation decision-theoretic rough sets. Int J Approx Reason 55:225–237
Wang F, Liang JY, Dang CY (2013) Attribute reduction for dynamic data sets. Appl Soft Comput 13:676–689
Liang JY, Wang F, Dang CY, Qian YH (2012) An efficient rough feature selection algorithm with a multi-granulation view. Int J Approx Reason 53:912–926
Davvaz B (2008) A short note on algebraic T-rough sets. Inf Sci 178:3247–3252
Li TJ (2008) Rough approximation operators on two universes of discourse and their fuzzy extensions. Fuzzy Sets Syst 159:3033–3050
Ali MI, Davvaz B, Shabir M (2013) Some properties of generalized rough sets. Inf Sci 224:170–179
Yao YY, Yao BX (2012) Covering based rough set approximations. Inf Sci 200:91–107
Liu GL, Sai Y (2010) Invertible approximation operators of generalized rough sets and fuzzy rough sets. Inf Sci 180:2221–2229
Liu GL (2010) Rough set theory based on two universal sets and its applications. Knowl Based Syst 23:110–115
Xu WH (2013) Fuzzy rough set models over two universes. Int J Mach Learn Cybern 4:631–645
Kelley JL (1995) General topology. Published by Van Nostrand
Zhu W, Wang FY (2007) On three types of covering rough sets. IEEE Trans Knowl Data Eng 19:1131–1144
Zakowski W (1983) Approximations in the space \((U, \pi )\). Demonstratio Mathematica IXV pp 761–769
Abo-Tabl EA (2013) Rough sets and topological spaces based on similarity. Int J Mach Learn Cybern 4:451–458
Zhu W, Wang SP (2011) Matroidal approaches to generalized rough sets based on relations. Int J Mach Learn Cybern 2:273–279
Acknowledgments
This work is supported by grants from National Natural Science Foundation of China under Grant (Nos. 61379021, 11301367, 11061004).
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Tan, A., Li, J. A kind of approximations of generalized rough set model. Int. J. Mach. Learn. & Cyber. 6, 455–463 (2015). https://doi.org/10.1007/s13042-014-0273-x
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DOI: https://doi.org/10.1007/s13042-014-0273-x