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第2期 汤建国,等:基于覆盖粗糙集的语言动力系统 .233. 描述小明的成绩还是显得有些宽泛,通常根据经验 matica Sinica,2005(6):32-40 或感觉将其更细致地表述为诸如“中上”或“良下” [6]莫红,王飞跃.基于词计算的语言动力系统及其稳定性 等。在现实生活中,人们的这种“经验”和“感觉”在 [J].中国科学:F辑,2009,39(2):254-268. 描述事物和表达信息时往往非常微妙,虽然其传递 [7]PAWLAK Z.Rough sets[J].International Journal of Com- 的是一种模糊的信息,但却并不让人感到费解。相 puter and Information Sciences,1982,11(5):341-356. [8]PAWLAK Z.Rough Sets:Theoretical aspects of reasoning 反,人们多数会更愿意接受这种描述。 about data M].Boston:Kluwer Academic Publishers, 那么在推理方法中,如何反映和实现自然语言 1991:1-79. 中类似人的这种“经验”和“感觉”呢?其实已有的 [9]ZAKOWSKI W.Approximations in the space(U,II)[J]. 很多方法都可以用来解决这个问题,比如概率的方 Demonstratio Mathematica,1983(16):761-769. 法、模糊集中的隶属度方法以及粗糙集中的描述距 [10]ZHU W,WANG F.Reduction and axiomization of covering 离的嫡等。但由于自然语言本身是灵活多变的,相 generalized rough sets[J].Information Sciences,2003, 同的一句话在不同场景或时间背景下意义会存在很 152:217-230. 大不同,所以在用这些方法解决这个问题是,还需要 [11]ZHU W,WANG F.Axiomatic systems of generalized rough 采取具体问题具体对待的方式来灵活处理。在后续 sets[C]//Proceedings of the 1st International Conference 的研究中,将对这一问题展开深入的分析和研究。 on Rough Sets and Knowledge Technology.Chongqing, China,2006:216-221. 5结束语 [12]ZHU W,WANG F.Covering based granular computing for conflict analysis[C]//IEEE International Conference on 本文利用覆盖粗糙集的方法对语言动力系统进 Intelligence and Security Informatics.San Diego,CA, 行建模,提出了分析和解决问题的推理方法,通过实 USA:2006:566-571. 例对其进行了阐述和验证,结果表明模型计算得出的 [13]ZHU W,WANG F.Relationships among three types of 结论与现实中的实际情况基本一致。在后续研究中, covering rough sets C]//IEEE International Conference 将对人在用自然语言描述事物时的模糊性修饰和表 on Granular Computing.Atlanta,GA,USA,2006:43-48. 述进行研究,以使模型的计算结果更加准确合理。 [14]ZHU W,WANG F.Topological properties in covering- based rough sets[C]//Proceedings of the 4th International 参考文献: Conference on Fuzzy Systems and Knowledge Discovery. Haikou,China,2007:289-293. [1]WANG Feiyue.Modeling,analysis and synthesis of linguis- [15]ZHU W,WANG F.On three types of covering-based rough tic dynamic systems:a computational theory[C]//IEEE In- sets[J].IEEE Transactions on Knowledge and Data Engi- ternational Workshop on Architecture for Semiotic Modeling neering,2007,19(8):1131-1143. and Situation Control in Large Complex Systems.Monterey, [16]ZHU W,WANG F.The fourth type of covering-based CA,1995:173-178. rough sets[].Information Sciences,2012,201:80-92. [2]王飞跃.词计算和语言动力学系统的计算理论框架[J]: [17]YAO YY,YAO B X.Covering based rough set approxima- 模式识别与人工智能,2001,14(4):377-384 tions[J].Information Sciences,2012,200:91-107. WANG Feiyue.Computing with words and a framework for [18]GE X,BAI X L.YUN Z Q.Topological characterizations computational linguistic dynamic systems[J].Pattern Rec- of covering for special covering-based upper approximation ognition and Artificial Intelligence,2001,14(4):377-384. operators[J].Information Sciences,2012,204:70-81. [3]WANG F Y.On the abstraction of conventional dynamic sys- [19]WANG L J,YANG X B,YANG J Y,et al.Relationships tems:from numerical analysis to linguistic analysis[J].In- among generalized rough sets in six coverings and pure re- formation Sciences,2005,171(1/2/3):233-259. flexive neighborhood system[J].Information Sciences, [4]WANG F Y,YANG T,MO H.On fixed points of linguistic 2012,207(10):66-78. dynamic systems[J].Journal of System Simulation,2002, [20]TANG J G,SHE K,WANG Y Q.Covering-based soft 14(11):1479-1485. rough sets[J].Journal of Electronic Science and Technol- [5]王飞跃.词计算和语言动力学系统的基本问题和研究 g,2011,9(2):118-123. [J].自动化学报,2005(6):32-40. [21]TANG J G,SHE K,ZHU W.The refinement in covering- WANG Feiyue.Fundamental issues in research of computing based rough sets [C]//Proceedings of the International with words and linguistic dynamic systems[J].Acta Auto- Conference on Granular Computing.Taipei,China,2011:描述小明的成绩还是显得有些宽泛,通常根据经验 或感觉将其更细致地表述为诸如“中上”或“良下” 等。 在现实生活中,人们的这种“经验”和“感觉”在 描述事物和表达信息时往往非常微妙,虽然其传递 的是一种模糊的信息,但却并不让人感到费解。 相 反,人们多数会更愿意接受这种描述。 那么在推理方法中,如何反映和实现自然语言 中类似人的这种“经验”和“感觉”呢? 其实已有的 很多方法都可以用来解决这个问题,比如概率的方 法、模糊集中的隶属度方法以及粗糙集中的描述距 离的熵等。 但由于自然语言本身是灵活多变的,相 同的一句话在不同场景或时间背景下意义会存在很 大不同,所以在用这些方法解决这个问题是,还需要 采取具体问题具体对待的方式来灵活处理。 在后续 的研究中,将对这一问题展开深入的分析和研究。 5 结束语 本文利用覆盖粗糙集的方法对语言动力系统进 行建模,提出了分析和解决问题的推理方法,通过实 例对其进行了阐述和验证,结果表明模型计算得出的 结论与现实中的实际情况基本一致。 在后续研究中, 将对人在用自然语言描述事物时的模糊性修饰和表 述进行研究,以使模型的计算结果更加准确合理。 参考文献: [1]WANG Feiyue. Modeling, analysis and synthesis of linguis⁃ tic dynamic systems: a computational theory[C] / / IEEE In⁃ ternational Workshop on Architecture for Semiotic Modeling and Situation Control in Large Complex Systems. Monterey, CA, 1995: 173⁃178. [2]王飞跃. 词计算和语言动力学系统的计算理论框架[ J]. 模式识别与人工智能, 2001, 14(4): 377⁃384. WANG Feiyue. Computing with words and a framework for computational linguistic dynamic systems[ J]. Pattern Rec⁃ ognition and Artificial Intelligence, 2001, 14(4): 377⁃384. [3]WANG F Y. On the abstraction of conventional dynamic sys⁃ tems: from numerical analysis to linguistic analysis[ J]. In⁃ formation Sciences, 2005, 171(1 / 2 / 3): 233⁃259. [4]WANG F Y, YANG T , MO H. On fixed points of linguistic dynamic systems[ J]. Journal of System Simulation, 2002, 14(11): 1479⁃1485. [5]王飞跃. 词计算和语言动力学系统的基本问题和研究 [J]. 自动化学报, 2005(6): 32⁃40. WANG Feiyue. Fundamental issues in research of computing with words and linguistic dynamic systems[ J]. Acta Auto⁃ matica Sinica, 2005(6): 32⁃40. [6]莫红,王飞跃. 基于词计算的语言动力系统及其稳定性 [J]. 中国科学: F 辑, 2009, 39(2): 254⁃268. [7]PAWLAK Z. Rough sets[ J]. International Journal of Com⁃ puter and Information Sciences, 1982, 11(5): 341⁃356. [8]PAWLAK Z. Rough Sets: Theoretical aspects of reasoning about data [ M ]. Boston: Kluwer Academic Publishers, 1991: 1⁃79. [9]ZAKOWSKI W. Approximations in the space(U,∏) [ J]. Demonstratio Mathematica, 1983(16): 761⁃769. [10]ZHU W, WANG F. Reduction and axiomization of covering generalized rough sets [ J]. Information Sciences, 2003, 152: 217⁃230. [11]ZHU W, WANG F. Axiomatic systems of generalized rough sets[C] / / Proceedings of the 1st International Conference on Rough Sets and Knowledge Technology. Chongqing, China, 2006: 216⁃221. [12]ZHU W, WANG F. Covering based granular computing for conflict analysis [ C] / / IEEE International Conference on Intelligence and Security Informatics. San Diego, CA, USA: 2006: 566⁃571. [13] ZHU W, WANG F. Relationships among three types of covering rough sets [ C] / / IEEE International Conference on Granular Computing. Atlanta, GA, USA, 2006: 43⁃48. [14] ZHU W, WANG F. Topological properties in covering⁃ based rough sets[C] / / Proceedings of the 4th International Conference on Fuzzy Systems and Knowledge Discovery. Haikou, China, 2007: 289⁃293. [15]ZHU W, WANG F. On three types of covering⁃based rough sets[J]. IEEE Transactions on Knowledge and Data Engi⁃ neering, 2007, 19(8): 1131⁃1143. [16] ZHU W, WANG F. The fourth type of covering⁃based rough sets[J]. Information Sciences, 2012, 201: 80⁃92. [17]YAO Y Y, YAO B X. Covering based rough set approxima⁃ tions[J]. Information Sciences, 2012, 200: 91⁃107. [18]GE X, BAI X L, YUN Z Q. Topological characterizations of covering for special covering⁃based upper approximation operators[J]. Information Sciences, 2012, 204: 70⁃81. [19]WANG L J , YANG X B, YANG J Y, et al. Relationships among generalized rough sets in six coverings and pure re⁃ flexive neighborhood system [ J ]. Information Sciences, 2012, 207(10): 66⁃78. [20] TANG J G, SHE K, WANG Y Q. Covering⁃based soft rough sets[J]. Journal of Electronic Science and Technol⁃ ogy, 2011, 9(2): 118⁃123. [21]TANG J G, SHE K, ZHU W. The refinement in covering⁃ based rough sets [ C] / / Proceedings of the International Conference on Granular Computing. Taipei, China, 2011: 第 2 期 汤建国,等:基于覆盖粗糙集的语言动力系统 ·233·
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