Three-way Decisions with Rough Membership Functions in Covering Approximation Space

• Autorzy: Yang Bin , Hu Bao Qing , Quiao Junsheng

Identyfikatory

DOI

10.3233/FI-2019-1780

• Języki publikacji: EN

Abstrakty

EN

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 give a new method to discuss three-way decisions with rough membership functions in covering approximation space. Firstly, we introduce three new types of rough membership functions and study their properties. And then, relationship between a covering and its derived fuzzy β-covering is investigated by using rough membership functions. In addition, we study the relationship among the four types of rough membership functions. Finally, a novel type of graded covering-based rough set model is proposed on the basis of rough membership function. And, as an application, its corresponding three-way decisions in incomplete decision systems are investigated.

Słowa kluczowe

EN

fuzzy β-covering; graded covering-based rough set; neighborhood; rough membership function; three-way decisions

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2019
• Tom: Vol. 165, nr 2
• Strony: 157--191
• Opis fizyczny: Bibliogr. 84 poz., tab.

Twórcy

autor

Yang Bin

• School of Mathematics and Statistics, Wuhan University, Wuhan 430072, PR China

autor

Hu Bao Qing

• School of Mathematics and Statistics, Wuhan University, Wuhan 430072, PR China

autor

Quiao Junsheng

• School of Mathematics and Statistics, Wuhan University, Wuhan 430072, PR China

Bibliografia

• [1] Boixader D, Jacas J, Recasens J. Upper and lower approximations of fuzzy sets. International Journal of General System, 2000.29:555-568. doi:10.1080/03081070008960961.
• [2] Bonikowski Z, Bryniarski E, Wybraniec-Skardowska U. Extensions and intentions in the rough set theory. Information Sciences, 1998.107:149-167. URL https://doi.org/10.1016/S0020-0255(97)10046-9.
• [3] Šešelja B. L-fuzzy covering relation. Fuzzy Sets and Systems, 2007.158:2456-2465.
• [4] Chakraborty MK. On fuzzy sets and rough sets from the perspective of indiscernibility. In: Indian Conference on Logic and Its Applications. Springer, 2011 pp. 22-37. doi:10.1007/978-3-642-18026-2_4.
• [5] Chen D, Zhang W, Yeung D, Tsang E. Rough approximations on a complete completely distributive lattice with applications to generalized rough sets. Information Sciences, 2006.176(13):1829-1848. URL https://doi.org/10.1016/j.ins.2005.05.009.
• [6] De Cock M, Cornelis C, Kerre E. Fuzzy rough sets: beyond the obvious. In: Proceedings IEEE International Conference on Fuzzy Systems., volume 1. 2004 pp. 103-108. doi:10.1109/FUZZY.2004.1375697.
• [7] Déer L, Verbiest N, Cornelis C, Godo L. A comprehensive study of implicatoryCconjunctor-based and noise-tolerant fuzzy rough sets: Definitions, properties and robustness analysis. Fuzzy Sets and Systems, 2015.275:1-38. doi:10.1016/j.fss.2014.11.018.
• [8] D'eer L, Cornelis C, Godo L. Fuzzy neighborhood operators based on fuzzy coverings. Fuzzy Sets and Systems, 2017.312:17-35. URL https://doi.org/10.1016/j.fss.2016.04.003.
• [9] Deng T, Chen Y, Xu W, Dai Q. A novel approach to fuzzy rough sets based on a fuzzy covering. Information Sciences, 2007.177(11):2308-2326. URL https://doi.org/10.1016/j.ins.2006.11.013.
• [10] Dubois D, Prade H. Rough fuzzy sets and fuzzy rough sets. International Journal of General Systems, 1990.17:191-201. URL https://doi.org/10.1080/03081079008935107.
• [11] Eells E, Fitelson B. Symmetries and asymmetries in evidential support. Philosophical Studies, 2002.107(2):129-142. doi:10.1023/A:1014712013453.
• [12] Fang BW, Hu BQ. Probabilistic graded rough set and double relative quantitative decision-theoretic rough set. International Journal of Approximate Reasoning, 2016.74:1-12. URL https://doi.org/10.1016/j.ijar.2016.03.004.
• [13] Feng T, Zhang S, Mi J. The reduction and fusion of fuzzy covering systems based on the evidence theory. International Journal of Approximate Reasoning, 2012.53(1):87-103. URL https://doi.org/10.1016/j.ijar.2011.10.002.
• [14] Ge X, Wang P, Yun Z. The rough membership functions on four types of covering-based rough sets and their applications. Information Sciences, 2017.390:1-14. URL https://doi.org/10.1016/j.ins.2017.01.032.
• [15] Greco S, Matarazzo B, Slowinski R. Rough approximation by dominance relations. International Journal of Intelligent Systems, 2002. 17:153-171. URL https://doi.org/10.1002/int.10014.
• [16] Greco S, Matarazzo B, Słowiński R. Parameterized rough set model using rough membership and Bayesian confirmation measures. International Journal of Approximate Reasoning, 2008.49(2):285-300. URL https://doi.org/10.1016/j.ijar.2007.05.018.
• [17] Grzymala-Busse JW. Rough set and CART approaches to mining incomplete data. In: Proceedings of International Conference of Soft Computing and Pattern Recognition (SoCPaR), Paris, France, 2010, pp: 214-219. doi:10.1109/SOCPAR.2010.5685860.
• [18] Grzymala-Busse JW, Clark PG, Kuehnhausen M. Generalized probabilistic approximations of incomplete data. International Journal of Approximate Reasoning, 2014.55(1):180-196. URL https://doi.org/10.1016/j.ijar.2013.04.007.
• [19] 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.
• [20] Hu BQ, Wong H. Generalized interval-valued fuzzy variable precision rough sets. International Journal of Fuzzy Systems, 2014.16(4):554-565.
• [21] Hu BQ. Three-way decisions space and three-way decisions. Information Sciences, 2014.281:21-52. URL https://doi.org/10.1016/j.ins.2014.05.015.
• [22] Hu BQ. Three-way decision spaces based on partially ordered sets and three-way decisions based on hesitant fuzzy sets. Knowledge-Based Systems, 2016.91:16-31. URL https://doi.org/10.1016/j.knosys.2015.09.026.
• [23] Hu BQ. Three-way decisions based on semi-three-way decision spaces. Information Sciences, 2017.382:415-440. doi:10.1016/j.ins.2016.12.012.
• [24] Järvinen J. On the structure of rough approximations. In: Rough Sets and Current Trends in Computing, volume 2475 of LNCS. 2002 pp. 123-130. doi:10.1007/3-540-45813-1_15.
• [25] Jensen R, Shen Q. Fuzzy-rough attributes reduction with application to web categorization. Fuzzy Sets and Systems, 2004.141(3):469-485. URL https://doi.org/10.1016/S0165-0114(03)00021-6.
• [26] Kondo M. On the structure of generalized rough sets. Information Sciences, 2006.176(5):589-600. URL https://doi.org/10.1016/j.ins.2005.01.001.
• [27] Kryszkiewicz M. Rules in incomplete information systems. Information Sciences, 1999.113(3-4):271-292. URL https://doi.org/10.1016/S0020-0255(98)10065-8.
• [28] Lang G, Li Q, Guo L. Homomorphisms between covering approximation spaces. Fundamenta Informaticae, 2015.138(3):351-371. doi:10.3233/FI-2015-1216.
• [29] Lang G, Miao D, Yang T, Cai M. Knowledge reduction of dynamic covering decision information systems when varying covering cardinalities. Information Sciences, 2016.346-347:236-260. URL https://doi.org/10.1016/j.ins.2016.01.099.
• [30] Lang G, Miao D, Cai M, Zhang Z. Incremental approaches for updating reducts in dynamic covering information systems. Knowledge-Based Systems, 2017.134:85-104. URL https://doi.org/10.1016/j.knosys.2017.07.020.
• [31] Lang G, Miao D, Cai M. Three-way decision approaches to conflict analysis using decision-theoretic rough set theory. Information Sciences, 2017.406-407:185-207. URL https://doi.org/10.1016/j.ins.2017.04.030.
• [32] Lang G, Cai M, Fujita H, Xiao Q. Related Families-baed attribute reduction of dynamic covering decision information systems. Knowledge-Based Systems, 2018. URL https://doi.org/10.1016/j.knosys2018.05.019.
• [33] Le VT, Hu BQ. Three-way decisions based on covering rough set. Journal of Intelligent & Fuzzy Systems, 2016.30(3):1763-1772. doi:10.3233/IFS-151887.
• [34] 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, 2007 pp. 55-62. doi:10.1007/978-3-540-72530-5_6.
• [35] Li TJ, Leung Y, Zhang WX. Generalized fuzzy rough approximation operators based on fuzzy coverings. International Journal of Approximate Reasoning, 2008.48(3):836-856. URL https://doi.org/10.1016/j.ijar.2008.01.006.
• [36] Li W, Miao D, Wang W, Zhang N. Hierarchical rough decision theoretic framework for text classification. In: Cognitive Informatics (ICCI), 2010 9th IEEE International Conference on. IEEE, 2010 pp. 484-489.
• [37] Li W, Xu W. Double-quantitative decision-theoretic rough set. Information Sciences, 2015.316:54-67. URL https://doi.org/10.1016/j.ins.2015.04.020.
• [38] Li Y, Zhang C, Swan JR. An information filtering model on the Web and its application in JobAgent. Knowledge-Based Systems, 2000.13(5):285-296. URL https://doi.org/10.1016/S0950-7051(00)00088-5.
• [39] Liang D, Liu D. A novel risk decision making based on decision-theoretic rough sets under hesitant fuzzy information. IEEE Transactions on Fuzzy Systems, 2015.23(2):237-247. doi:10.1109/TFUZZ.2014.2310495.
• [40] Liang D, Liu D, Pedrycz W, Hu P. Triangular fuzzy decision-theoretic rough sets. International Journal of Approximate Reasoning, 2013. 54:1087-1106.
• [41] Lingras P, Chen M, Miao D. Rough cluster quality index based on decision theory. IEEE Transactions on Knowledge and Data Engineering, 2009.21(7):1014-1026. doi:10.1109/TKDE.2008.236.
• [42] Liu D, Yao Y, Li T. Three-way investment decisions with decision-theoretic rough sets. International Journal of Computational Intelligence Systems, 2011.4(1):66-74. doi:10.2991/ijcis.2011.4.1.6.
• [43] Liu D, Li T, Liang D. Three-way government decision analysis with decision-theoretic rough sets. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2012.20:119-132. URL https://doi.org/10.1142/S0218488512400090.
• [44] Ma L. Some twin approximation operators on covering approximation spaces. International Journal of Approximate Reasoning, 2015.56:59-70. URL https://doi.org/10.1016/j.ijar.2014.08.003.
• [45] Ma L. Two fuzzy covering rough set models and their generalizations over fuzzy lattices. Fuzzy Sets and Systems, 2016.294:1-17. URL https://doi.org/10.1016/j.fss.2015.05.002.
• [46] Mi J, Zhang W. An axiomatic characterization of a fuzzy generalization of rough sets. Information Sciences, 2004.160(1-4):235-249. URL https://doi.org/10.1016/j.ins.2003.08.017.
• [47] Pawlak Z. Rough sets. International Journal of Computer and Information Sciences, 1982.11:341-356.
• [48] Pawlak Z. Rough sets: theoretical aspects of reasoning about data. Kluwer Academic Publishers, Boston, 1991. ISBN-10:0792314727, 13:978-0792314721.
• [49] Pawlak Z. Fuzzy sets and rough sets. Fuzzy Sets and Systems, 1985.17:99-102.
• [50] Pawlak Z, Skowron A. Rough membership functions. In: Advances in the Dempster-Shafer theory of evidence. John Wiley & Sons, Inc., 1994 pp. 251-271. ISBN-0-471-55248-8.
• [51] Pawlak Z. Some issues on rough sets. In: Transactions on Rough Sets I, Springer 2004 pp. 1-58. doi:10.1007/978-3-540-27794-1_1.
• [52] Pomykala J. Approximation operations in approximation space. Bulletin of the Polish Academy of Sciences, 1987.35:653-662.
• [53] Pomykała J. On definability in the nondeterministic information system. Bulletin of the Polish Academy of Sciences. Mathematics, 1988.36:193-210.
• [54] Qin K, Gao Y, Pei Z. On covering rough sets. In: Rough Set and Knowledge Technology, LNCS 2007 pp. 34-41. doi:10.1007/978-3-540-72458-2_4.
• [55] Radzikowska A, Kerre E. A comparative study of fuzzy rough sets. Fuzzy Sets and Systems, 2002.126(2):137-155. URL https://doi.org/10.1016/S0165-0114(01)00032-X.
• [56] Radzikowska AM, Kerre EE. Fuzzy rough sets based on residuated lattices. In: Transactions on Rough Sets, volume 3135 of LNCS. 2004 pp. 278-296. doi:10.1007/978-3-540-27778-1_14.
• [57] Skowron A, Stepaniuk J. Tolerance approximation spaces. Fundamenta Informaticae, 1996.27:245-253.
• [58] Slowinski R, Vanderpooten D. A generalized definition of rough approximations based on similarity. IEEE Transactions on Knowledge and Data Engineering, 2000.12(2):331-336. doi:10.1109/69.842271.
• [59] Wang C, Chen D, Hu Q. Fuzzy information systems and their homomorphisms. Fuzzy Sets and Systems, 2014.249:128-138. URL https://doi.org/10.1016/j.fss.2014.02.009.
• [60] Wang C, Shao M, He Q, Qian Y, Qi Y. Feature subset selection based on fuzzy neighborhood rough sets. Knowledge-Based Systems, 2016.111(1):173-179. URL https://doi.org/10.1016/j.knosys.2016.08.009.
• [61] Wang C, Chen D, Sun B, Hu Q. Communication between information systems with covering based rough sets. Information Sciences, 2012.216:17-33. URL https://doi.org/10.1016/j.ins.2012.06.010.
• [62] Wang X, Tsang EC, Zhao S, Chen D, Yeung DS. Learning fuzzy rules from fuzzy samples based on rough set technique. Information Sciences, 2007.177(2):4493-4514. URL https://doi.org/10.1016/j.ins.2007.04.010.
• [63] Wu W, Zhang W. Neighborhood operator systems and approximations. Information Sciences, 2002.144(1-4):263-282. URL https://doi.org/10.1016/S0020-0255(02)00180-9.
• [64] Wu W, Zhang W. Constructive and axiomatic approaches of fuzzy approximation operators. Information Sciences, 2004.159(3-4):233-254. URL https://doi.org/10.1016/j.ins.2003.08.005.
• [65] Xu J, Miao D, Zhang Y, Zhang Z. A three-way decisions model with probabilistic rough sets for stream computing. International Journal of Approximate Reasoning, 2017.88:1-22. URL https://doi.org/10.1016/j.ijar.2017.05.001.
• [66] Yang B, Hu BQ. A fuzzy covering-based rough set model and its generalization over fuzzy lattice. Information Sciences, 2016.367-368(1):463-486. URL https://doi.org/10.1016/j.ins.2016.05.053.
• [67] Yang B, Hu BQ. On some types of fuzzy covering-based rough sets. Fuzzy Sets and Systems, 2017.312:36-65. URL https://doi.org/10.1016/j.fss.2016.10.009.
• [68] Yang B, Zhu W. A New Type of Covering-Based Rough Sets. In: International Conference on Rough Sets and Knowledge Technology. Springer, 2014 pp. 489-499. doi:10.1007/978-3-319-11740-9_45.
• [69] Yao J, Azam N. Web-based medical decision support systems for three-way medical decision making with game-theoretic rough sets. IEEE Transactions on Fuzzy Systems, 2015.23(1):3-15. doi:10.1109/TFUZZ.2014.2360548.
• [70] Yao YQ, Mi JS, Li ZJ. Attribute reduction based on generalized fuzzy evidence theory in fuzzy decision systems. Fuzzy Sets and Systems, 2011.170(1):64-75. URL https://doi.org/10.1016/j.fss.2011.01.008.
• [71] Yao Y. Constructive and algebraic methods of theory of rough sets. Information Sciences, 1998.109(1-4):21-47. URL https://doi.org/10.1016/S0020-0255(98)00012-7.
• [72] Yao Y. Relational interpretations of neighborhood operators and rough set approximation operators. Information Sciences, 1998.111(1-4):239-259. URL https://doi.org/10.1016/S0020-0255(98)10006-3.
• [73] Yao Y, Yao B. Covering based rough set approximations. Information Sciences, 2012.200:91-107. URL https://doi.org/10.1016/j.ins.2012.02.065.
• [74] Yao Y. A comparative study of fuzzy sets and rough sets. Information Sciences, 1998.109(1-4):227-242. URL https://doi.org/10.1016/S0020-0255(98)10023-3.
• [75] Yao Y. Probabilistic rough set approximations. International Journal of Approximate Reasoning, 2008.49(2):255-271. URL https://doi.org/10.1016/j.ijar.2007.05.019.
• [76] Yao Y. Three-way decisions with probabilistic rough sets. Information Sciences, 2010.180(3):341-353. URL https://doi.org/10.1016/j.ins.2009.09.021.
• [77] Yao Y, Lin T, Zimmermann H. Graded rough set approximations based on nested neighborhood systems. In: Proceedings of 5th European Congress on intelligent techniques and Soft computing, volume 1. Verlag Mainz, 1997 pp. 196-200.
• [78] Yu H, Liu Z, Wang G. An automatic method to determine the number of clusters using decision-theoretic rough set. International Journal of Approximate Reasoning, 2014.55(1):101-115. URL https://doi.org/10.1016/j.ijar.2013.03.018.
• [79] Yu H, Zhang C, Wang G. A tree-based incremental overlapping clustering method using the three-way decision theory. Knowledge-Based Systems, 2016.91:189-203. URL https://doi.org/10.1016/j.knosys.2015.05.028.
• [80] Zadeh L. Fuzzy sets. Information and Control, 1965.8(3):338-358. URL https://doi.org/10.1016/S0019-9958(65)90241-X.
• [81] Zakowski W. Approximations in the space (U;Π). Demonstratio Mathematica, 1983.16:761-769. URL https://doi.org/10.1515/dema-1983-0319.
• [82] Zhang HR, Min F. Three-way recommender systems based on random forests. Knowledge-Based Systems, 2016.91:275-286. URL https://doi.org/10.1016/j.knosys.2015.06.019.
• [83] Zhu W, Wang F. Reduction and axiomization of covering generalized rough sets. Information Sciences, 2003.152:217-230. URL https://doi.org/10.1016/S0020-0255(03)00056-2.
• [84] Zhu W. Relationship among basic concepts in covering-based rough sets. Information Sciences, 2009.179(14):2478-2486. URL https://doi.org/10.1016/j.ins.2009.02.013.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).