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Tytuł artykułu

Neighborhood Systems and Variable Precision Generalized Rough Sets

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we present the connection between the concepts of Variable Precision Generalized Rough Set model (VPGRS-model) and Neighborhood Systems through binary relations. We provide characterizations of lower and upper approximations for VPGRS-model by introducing minimal neighborhood systems. Furthermore, we explore generalizations by investigating variable parameters which are limited by variable precision. We also prove some properties of lower and upper approximations for VPGRS-model.
Wydawca
Rocznik
Strony
271--290
Opis fizyczny
Bibliogr. 27 poz.
Twórcy
autor
  • Department of Information Management, National Formosa University, Huwei 63201, Yunlin, Taiwan
autor
  • Department of Mathematics, Central Michigan University Mt. Pleasant, Michigan 48859, USA
autor
  • Institute of Information, Science Academia Sinica, Nankang 115, Taipei, Taiwan
Bibliografia
  • [1] Csajbók Z. Approximations of sets based on partial covering, Theoretical Computer Science, 2011; 412(42):5820–5833. URL https://doi.org/10.1016/j.tcs.2011.05.037.
  • [2] Csajbók Z. Approximations of sets based on partial covering, PhD thesis, University of Debrecen, Debrecen, 2011.
  • [3] Clark PG, Grzymala-Busse JW, Rzasa W. Consistency of incomplete data, Information Sciences, 2015;322:197–222. URL https://doi.org/10.1016/j.ins.2015.06.011.
  • [4] Day MM. Convergence, closure, and neighborhoods, Duke Mathematical Journal, 1944;11(1):181–199. doi:10.1215/S0012-7094-44-01118-X.
  • [5] Dutta S, Skowron A. Generalized quantifiers in the context of rough set, Fundamenta Informaticae, 2015;142(1-4):213–236. doi:10.3233/FI-2015-1292.
  • [6] Fan TF, Liau CJ, Liu DR. A uniform framework for rough approximations based on generalized quantifiers, Transactions on Rough Sets, 2015;19:1–16. doi:10.1007/978-3-662-47815-8_1.
  • [7] Gong Z, Xiao Z. Variable precision rough set model based on general relations, Proceedings of the 2004 IEEE International Conference on Machine Learning and Cybernetics, 2004, pp. 2490–2494. doi:10.1109/ICMLC.2004.1382222.
  • [8] Gong Z, Shi Z, Yao H. Variable precision rough set model for incomplete information systems and its β-reducts, Computing and Informatics, 2012;31(6):1385–1399.
  • [9] Grzymala-Busse JW, Clark PG, Kuehnhausen M. Generalized probabilistic approximations of incomplete data, International Journal of Approximate Reasoning, 2014;55(1):180–196. doi:10.1016/j.ijar.2013.04.007.
  • [10] Järvinen J. Pawlak’s information systems in terms of Galois connections and functional dependencies, Fundamenta Informaticae, 2007;75(1-4):315–330.
  • [11] Järvinen J. Properties of rough approximations, Journal of Advanced Computational Intelligence and Intelligent Informatics, 2005;9:502–505. doi:10.20965/jaciii.2005.p0502(2005).
  • [12] Keenan D, Westerståhl D. Generalized quantifiers in linguistics and logic, in Handbook of Logic and Language (J. Van Benthem, A. ter Meulen, Eds.), Elsevier, 2011, pp. 859–910. doi:10.1016/B978-0-444-53726-3.00019-0.
  • [13] Kryszkiewicz M. Rough set approach to incomplete information system, Information Sciences, 1998;112(1-4):39–49. URL https://doi.org/10.1016/S0020-0255(98)10019-1.
  • [14] Liau CJ. Modal reasoning and rough set theory, Proceedings of 8th International Conference on Artificial Intelligence: Methodology, Systems, and Applications (AIMSA), 1998, pp. 317–330. doi:10.1007/BFb0057455.
  • [15] Liau CJ. An overview of rough set semantics for modal and quantifier logics, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2000;8(1):93–118. URL http://dx.doi.org/10.1142/S0218488500000071.
  • [16] Lin TY. Granular computing for binary relations: clustering and axiomatic granular operators, Proceedings of the North American Fuzzy Information Processing Society, 2004, pp. 430–433. doi:10.1109/NAFIPS.2004.1336321.
  • [17] Lin TY. Granular computing on binary relations I: data mining and neighborhood systems, in: Rough Sets and Knowledge Discovery (A. Skowron, L. Polkowski, Eds.), Physica-Verlag, 1998, pp. 107-121.
  • [18] Lin TY, Syau YR. Granular mathematics-foundation and current state, Proceedings of the 2011 IEEE International Conference on Granular Computing, 2011, pp. 4–12. doi:10.1109/GRC.2011.6122560.
  • [19] Liu G, Zhu W. The algebraic structures of generalized rough set theory. Information Sciences, 2008; 178(21):4105–4113. URL https://doi.org/10.1016/j.ins.2008.06.021.
  • [20] Pawlak Z. Rough Sets: Theoretical Aspects of Reasoning About Data, Kluwer Academic Publishers, Dordrech, 1991. ISBN-978-0-7923-1472-1.
  • [21] Pawlak Z. Rough sets, International Journal of Computer and Information Science, 1982;11(5):341–356. doi:10.1007/BF01001956.
  • [22] Peters S, Westerståhl D. Quantifiers in Language and Logic, Clarendon Press, 2006. ISBN-019929125X.
  • [23] Slezak D. Rough sets and Bayes factor, Transactions on Rough Sets, III, 2005, pp. 202–229. doi:10.1007/11427834_10.
  • [24] Slezak D, Ziarko W. The investigation of the Bayesian rough set model, International Journal of Approximate Reasoning, 2005;40(1-2):81–91. URL https://doi.org/10.1016/j.ijar.2004.11.004.
  • [25] Syau YR, Skowron A, Lin EB. Inclusion degree with variable-precision model in analyzing inconsistent decision tables. Granular Computing, 2017;2(2):65–72. doi:10.1007/s41066-016-0027-0.
  • [26] Yao Y, Lin TY. Generalization of rough sets using modal logics, Intelligent Automation and Soft Computing, An International Journal, 1996;2(2):103–120. URL http://dx.doi.org/10.1080/10798587.1996.10750660.
  • [27] Ziarko W. Variable precision rough set model. Journal of Computer and System Sciences, 1993;46(1):39–59. URL https://doi.org/10.1016/0022-0000(93)90048-2.
Uwagi
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
Typ dokumentu
Bibliografia
Identyfikator YADDA
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