粗糙集理论：基于三支决策视角

南京大学学报(自然科学版) ›› 2013, Vol. 49 ›› Issue (5): 574–581.

粗糙集理论：基于三支决策视角

刘盾1, 李天瑞2, 李华雄3

出版日期:2014-01-21 发布日期:2014-01-21
作者简介:(西南交通大学经济管理学院成都610031;2. 西南交通大学信息科学与技术学院成都610031; 3. 南京大学工程管理学院南京, 210093)
基金资助:
国家自然科学基金(71201133,71201076),高校博士点基金(20120184120028),教育部人文社科基金
(11YJC630127),中国博士后科研基金(2012M520310,2013T60132),中央高校基本科研业务费专项资金
(SWJTU12CX117),江苏省自然科学基金(BK2011564)

Rough set theory: A three-way decisions perspective

Liu Dun1, Li Tian-Rui2, Li Hua-Hiong3

Online:2014-01-21 Published:2014-01-21
About author:(1. School of Economics and Management, Southwest Jiaotong University, Chengdu, 610031, China; 2. School of Information Science and Technology, Southwest Jiaotong University, Chengdu, 610031, China; 3. School of Management and Engineering, Nanjing University, Nanjing, 210093)

摘要/Abstract

摘要： 从三支决策的视角出发，系统地介绍了三支决策与粗糙集理论相融合的理论、方法和应用。考虑到粗糙集理论中的正域、负域和边界域可分别生成相应的接受、拒绝和延迟决策规则，三支决策赋予粗糙集新的语义解释。通过分析三支决策与概率粗糙集、决策粗糙集间的关系；三支决策与二支决策、多支决策的关系以及三支决策在扩展模型、属性约简和规则推导方法在信息工程管理医学等方面的应用，给出三支决策研究的现状。最后，指出了三支决策发展的未来方向。

Abstract: From the perspective of three-way decisions, the theory, methodology and applications of rough setsreinterpreted and systematically investigated. The three regions of rough sets can generate rules of acceptance, rejection and deferment, respectively, which provides a new semantic explanation of rough sets. The current researches of three-way decisions are carefully investigated via five different aspects: a) the relationships among three-way decisions, probabilistic rough sets and decision-theoretic rough sets; b) the relationships among three-way decisions, two-way decisions and multi-way decisions; c) the extended models of three-way decisions, d) the attributes reduction and rules acquisition of three-way decisions, and e) the applications of three-way decisions in different domains. Finally, we point out future researches on three-way decisions.

刘盾1, 李天瑞2, 李华雄3. 粗糙集理论：基于三支决策视角[J]. 南京大学学报(自然科学版), 2013, 49(5): 574–581.

Liu Dun1, Li Tian-Rui2, Li Hua-Hiong3. Rough set theory: A three-way decisions perspective[J]. Journal of Nanjing University(Natural Sciences), 2013, 49(5): 574–581.

参考文献

[1] Yao Y Y. Three-way decisions with probabilistic rough sets. Information Sciences, 2010, 180, 341~353.
[2] Yao Y Y. The superiority of three-way decision in probabilistic rough set models. Information Sciences, 2011, 181, 1080~1096.
[3] Liu D, Li T R, Miao D, et al. Three-way decisions and granular computing. Bejing: Science Publishing, 2013, 332. (刘盾，李天瑞，苗夺谦等。三支决策与粒计算. 北京: 科学出版社，2013，332).
[4] Jia X Y, Shan L, Zhou X Z, et al. The theory and application of three-way decisions. Nanjing: Nanjing University Publishing, 2012, 218. (贾修一，商琳，周献中等. 三支决策理论与应用. 南京: 南京大学出版社，2012, 218).
[5] Li H X, Zhou X Z, Li T R, et al. Decision-theoretic rough sets and its research progress. Bejing: Science Publishing, 2011, 183. (李华雄，周献中，李天瑞等. 决策粗糙集理论及其研究进展. 北京: 科学出版社，2011，183).
[6] Liu D, Li T R, Ruan D. Probabilistic model criteria with decision-theoretic rough sets. Information Sciences, 2011, 181(17): 3709~3722.
[7] Yao Y Y, Wong S K M. A decision theoretic framework for approximating concepts. International Journal of Man-Machine Studies, 1992, 37: 793~809.
[8] Liu D, Li H X, Zhou X Z. Two decades’ research on decision-theoretic rough sets. Proceedings of the 9th IEEE International Conference on Cognitive Informatics, 2010: 968~973.
[9] Li H X, Liu D, Zhou X Z. Review on decision-theoretic rough set model. Journal of Chongqing University of Posts and Telecommunications (Natural Science Edition), 2010，22(5): 624~630. (李华雄，刘盾，周献中. 决策粗糙集模型研究综述. 重庆邮电大学学报(自然科学版)，2010，22(5): 624~630).
[10] Liu D, Li T R, Liang D C. Decision-theoretic rough sets with probabilistic distribution. Proceedings Rough Set and Knowledge Technology, LNAI 7414, 2012: 389~398.
[11] Liu D, Li T R, Li H X. Interval-valued decision-theoretic rough sets. Computer Science, 2012, 39(7): 178~181, 214. (刘盾，李天瑞，李华雄. 区间决策粗糙集. 计算机科学, 2012, 39(7): 178~181, 214).
[12] Liu D, Li T R, Liang D C. Fuzzy decision theoretic rough sets. Computer Science, 2012, 39(12): 25~29. (刘盾，李天瑞，梁德翠. 模糊数决策粗糙集. 计算机科学, 2012, 39(12): 25~29).
[13] Liang D C, Liu D, Pedrycz W. Triangular fuzzy decision-theoretic rough sets. International Journal of Approximate Reasoning, 2013, 54, 1087~1106.
[14] Yao Y Y. Some research problems of three-way decisions. Liu D, Li T R, Miao D, et al. Three-way decisions and granular computing. Bejing: Science Publishing, 2013, 1~13. (姚一豫. 三支决策研究的若干问题. 刘盾，李天瑞，苗夺谦等. 三支决策与粒计算. 北京：科学出版社, 2013, 1~13).
[15] Lingras P, Chen M, Miao D Q. Rough cluster quality index based on decision theory. IEEE Transactions on Knowledge and Data Engineering, 2009, 21: 1014~1026.
[16] Liu D, Li T R, Li H X. A multiple-category classification approach with decision-theoretic rough sets. Fundamenta Informaticae, 2012, 115(2-3): 173~188.
[17] Zhou B. Multi-class decision-theoretic rough sets. International Journal of Approximate Reasoning, 2013, DOI: 10.1016/j.ijar.2013.04.006.
[18] Abd El-Monsef M M E, Kilany N M. Decision analysis via granulation based on general binary relation. International Journal of Mathematics and Mathematical Sciences, 2007, Article ID: 12714.
[19] Yao Y Y, Deng X F. Sequential three-way decisions with probabilistic rough sets. Proceeding of the 10th IEEE International Conference on Cognitive Informatics, 2011: 120~125.
[20] Liu D, Yao Y Y, Li T R. Three-way decision-theoretic rough sets. Computer Science, 2011, 38(1): 246~250. (刘盾，姚一豫，李天瑞. 三枝决策粗糙集. 计算机科学, 2011, 38(1): 246~250).
[21] Greco S, Matarazzo B, Slowinski R. Parameterized rough set model using rough membership and Bayesian confirmation measures. International Journal of Approximate Reasoning, 2008, 49: 285~300.
[22] Gong Z T, Shi Z H. On the covering probabilistic rough set models and its Bayes decisions. Fuzzy Systems and Mathematics, 2008, 22(4): 142~148. (巩增泰, 史战红. 基于覆盖的概率粗糙集模型及其Bayes决策. 模糊系统与数学, 2008, 22(4): 142~148).
[23] Ma W M, Sun B Z. On relationship between probabilistic rough set and Bayesian risk decision over two universes. International Journal of General Systems, 2012, 41(3): 225~245.
[24] Yang X P, Yao J T. Modeling multi-agent three-way decisions with decision-theoretic rough sets. Fundamenta Informaticae, 2012, 115:157~171.
[25] Herbert J P, Yao J T. Game-theoretic rough sets. Fundamenta Informaticae, 2011, 108: 267~286.
[26] Yao Y Y, Zhou B. Naive bayesian rough sets . Proceeding of Rough Set and Knowledge Technology, LNAI 6401, 2010: 719~726.
[27] Li H X, Zhou X Z. Risk decision making based on decision-theoretic rough set: A three-way view decision model. International Journal of Computational Intelligence Systems, 2011, 4(1), 1~11.
[28] Liu D, Li T R, Liang D C. Incorporating logistic regression to decision-theoretic rough sets for classifications. International Journal of Approximate Reasoning, 2013, DOI: 10.1016/j.ijar.2013.02.013.
[29] Yao Y Y, Zhao Y. Attribute reduction in decision-theoretic rough set models. Information Sciences, 2008, 178: 3356~3373.
[30] Li H X, Zhou X Z, Zhao J B, et al. Non-monotonic attribute reduction in decision-theoretic rough sets. Fundamenta Informaticae, 2013, 126: 415~432.
[31] Jia X Y, Liao W H, Tang Z M, et al. Minimum cost attribute reduction in decision-theoretic rough set models. Information Sciences, 2013, 219: 151~167.
[32] Zhou B, Yao Y Y. In search for effective granularity with DTRS. Proceedings of the 9th IEEE International Conference on Cognitive Informatics, 2010: 464~470.
[33] Grzymala-Busse J W, Marepally S R, Yao Y Y. A comparison of positive, boundary, and possible rules using the MLEM2 rule induction algorithm. Proceedings of the 10th International Conference on Hybrid Intelligent Systems, 2010: 7~12.
[34] Grzymala-Busse J W, Yao Y Y. Probabilistic rule induction with the LERS data mining system. International Journal of Intelligent Systems, 2011, 26: 518~539.
[35] Min F, He H P, Qian Y H, et al. Test-cost-sensitive attribute reduction. Information Sciences, 2011, 181, 4928~4942.
[36] Zhao W Q, Zhu Y L. An email classification scheme based on decision-theoretic rough set theory and analysis of email security. Proceedings of the International Technical Conference of IEEE Region 10, doi:10.1109/TENCON. 2005.301121.
[37] Zhou B, Yao Y Y, Luo J G. A three-way decision approach to email spam filtering. Proceedings of the 23th Canadian Conference on Artificial Intelligence, 2010, LNAI 6085, 28~39.
[38] Miao D Q, Gao C, Zhang N. The Semi-supervised learning method with three-way decision theory. Jia X Y, Shan L, Zhou X Z, et al. The theory and application of three-way decisions. Nanjing: Nanjing University Press, 2012, 17~33. (苗夺谦，高灿，张楠. 基于三支决策理论的半监督学习. 贾修一，商琳，周献中等. 三支决策理论与应用. 南京: 南京大学出版社, 2012, 17~33).
[39] Yu H, Liu Z G, Wang G Y. An automatic method to determine the number of clusters using decision-theoretic rough set. International Journal of Approximate Reasoning, 2013, DOI: 10.1016/j.ijar.2013.03.018.
[40] Ayad R A, Liu J. Supporting E-learning system with modified bayesian rough set model. Proceedings of the 6th International Symposium on Neural Networks, 2009, LNCS 5552, 192~200.
[41] Li Y, Zhang C, Swan J. An information fltering model on the web and its application in JobAgent. Knowledge-Based Systems, 2000, 13, 285~296.
[42] Slezak D, Wroblewski J, Eastwood V. Brighthouse: An analytic data warehouse for ad-hoc queries. Proceeding of the Very Large Data Base Endowment, 2008: 1337~1345,
[43] Woodward P, Naylor J. An application of Bayesian methods in SPC. The Statistician, 1993, 42: 461~469.
[44] Yusgiantoro P, Hsiao F. Production-sharing contracts and decision making in oil production. Energy Economics, 1993, 10: 245~256.
[45] Forster M. Key concepts in model selection: Performance and generalizability. Journal of Mathematic Psychology, 2000, 44: 205~231.
[46] Liu D, Yao Y Y, Li T R. Three-way investment decisions with decision-theoretic rough sets. International Journal of Computational Intelligence Systems, 2011, 4(1): 66~74.
[47] Liu D, Li T R, Liang D C. Three-way government decision analysis with Decision-theoretic rough sets. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2012, 20(Supp. 1): 119~132.
[48] Savage L J. The Foundations of Statistics. New York: Dover Publications, 1972, 310.
[49] Goudey R. Do statistical inferences allowing three alternative decision give better feedback for environ-mentally precautionary decision-making. Journal of Environmental Management, 2007, 85: 338~344.
[50] Matthews L R, Bennett P G. The art of course planning: Soft O.R. in action. The Journal of the Operational Research Society, 1986, 37: 579~590.
[51] Weller A C. Editorial peer review: its strengths and weaknesses. Medford, NJ: Information Today, Inc., 2001, 342.
[52] Pauker S, Kassirer J. The threshold approach to clinical decision making. The New England Journal of Medicine, 1980, 302: 1109~1117.
[53] Yao J T, Herbert J P. Web-based support systems with rough set analysis. Proceeding of International Conference on Rough Set and Emerging Intelligent System Paradigms, LNAI 4585, 2007: 360~370.

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