第1期 杨洁，等：基于知识距离的粗糙粒结构的评价模型 ·173· 利用该结论，本文建立了一种在属性代价约束条 机学报，2015(8)：1497-1517. 件下的粗糙粒结构的评价模型，解决了在不同约 XU Ji,WANG Guoyin,YU Hong.Review of big data 束条件下评价并选择不同粗糙粒结构的问题。由 processing based on granular computing[J].Chinese 于本文采用的是基于EMD的知识距离框架，因 journal of computers,2015(8):1497-1517 此，本文的方法具有扩展性，可以针对不同类型 [12]YAO Yiyu.Three-way decisions with probabilistic rough 的粒结构设计评价模型，例如，对不同层次聚类 sets[J].Information sciences,2010,180(3):341-353. 算法、多尺度图像分割算法以及多粒度社区发现 [13]QIAN Yuhua,LIANG Jiye,YAO Yiyu,et al.MGRS:a 算法的评价和选择。但是，本文的工作还处于初 multi-granulation rough set[]].Information sciences, 步阶段，仅研究了如何评价粗糙粒结构，并没有 2010,1806:949-970. 考虑粗糙粒结构的构建问题，并且只考虑了属性 [14]QIAN Yuhua,LIANG Jiye,DANG Chuangyin.Incom- 代价为约束条件，评价模型的目标函数还有待进 plete multigranulation rough set[J].IEEE transactions on 一步改进，尤其如何根据不同的约束条件设计目 systems,man,and cybernetics-part A:systems and hu- 标函数是下一步工作的主要目标。 mans.2010,40(2):420-431. [15]QIAN Yuhua,CHENG Honghong,WANG Jieting,et al 参考文献： Grouping granular structures in human granulation intelli- [1]ZADEH L A.Toward a theory of fuzzy information granu- gence[J].Information sciences,2017,382-383:150-169. lation and its centrality in human reasoning and fuzzy lo- [16]张钹，张铃.问题求解理论及应用M.北京：清华大学 gic[J].Fuzzy sets and systems,1997,90(2):111-127 出版社，1990 [2]PEDRYCZ W.SKOWRON A.KREINOVICH V.Hand- [17]ZHANG Ling,ZHANG Bo.The structure analysis of book of granular computing[M].Chichester:John Wiley fuzzy sets[J].International journal of approximate reason- Sons.2008:719-740. ing,2005,40(1/2:92-108 [3]PEDRYCZ W.AL-HMOUZ R,MORFEQ A,et al.The [18]ZHANG Ling,ZHANG Bo.Fuzzy reasoning model un- design of free structure granular mappings:the use of the der quotient space structure[J].Information sciences, principle of justifiable granularity[J].IEEE transactions on 2005,173(4):353-364. cybernetics,2013,43(6):2105-2113 [19]WIERMAN M J.Measuring uncertainty in rough set the- [4]WANG Guoyin,YANG Jie,XU Ji.Granular computing: ory[J].International journal of general systems,1999, from granularity optimization to multi-granularity joint 28(4/5):283-297. problem solving[J].Granular computing,2017,2(3): [20]LIANG Jiye,CHIN K S,DANG Chuangyin,et al.A new 105-120 method for measuring uncertainty and fuzziness in rough [5]YAO Yiyu.Perspectives of granular computing[C]//Pro- set theory[J].International journal of general systems, ceedings of 2015 IEEE International Conference on Granu- 2002,31(4):331-342 lar Computing.Beijing,China,2005:85-90. [21]YAO Yiyu,ZHAO Liquan.A measurement theory view [6]ZADEH L A.Fuzzy sets[].Information and control,1965. on the granularity of partitions[J].Information sciences, 8(3):338-353 2012.213:1-13 [7]PAWLAK Z.Rough sets[J].International journal of com- [22]LAWVERE F W.Metric spaces,generalized logic,and puter&information sciences,1982,11(5):341-356 closed categories[J].Rendiconti del seminario matem- [8]张钹，张铃.问题求解理论及应用M北京：清华大学出 atico e fisico di milano,1973,43(1):135-166. 版社，1990. [23]RUBNER Y.GUIBAS L.TOMASI C.The earth mover's [9]李德毅，孟海军，史雪梅.隶属云和隶属云发生器几.计 distance,multi-dimensional scaling,and color-based im- 算机研究与发展，19956)：15-20. age retrieval[Cl/Proceedings of the ARPA Image Under- LI Deyi,MENG Haijun,SHI Xuemei.Membership clouds standing Workshop.1997:661-668. and membership cloud generators[J.Journal of computer [24]RUBNER Y.TOMASI C.GUIBAS L J.The earth research and development,1995(6):15-20. mover's distance as a metric for image retrieval[J].Inter- [10]苗夺谦，李德毅，姚一豫，等.不确定性与粒计算M北 national journal of computer vision,2000,40(2):99-121. 京：科学出版社，2011. [25]郭增晓，米据生.粗糙模糊集的模糊性度量J刀.模糊系 [11]徐计，王国胤，于洪.基于粒计算的大数据处理).计算 统与数学，2005,19(4)：135-140.利用该结论，本文建立了一种在属性代价约束条 件下的粗糙粒结构的评价模型，解决了在不同约 束条件下评价并选择不同粗糙粒结构的问题。由 于本文采用的是基于 EMD 的知识距离框架，因 此，本文的方法具有扩展性，可以针对不同类型 的粒结构设计评价模型，例如，对不同层次聚类 算法、多尺度图像分割算法以及多粒度社区发现 算法的评价和选择。但是，本文的工作还处于初 步阶段，仅研究了如何评价粗糙粒结构，并没有 考虑粗糙粒结构的构建问题，并且只考虑了属性 代价为约束条件，评价模型的目标函数还有待进 一步改进，尤其如何根据不同的约束条件设计目 标函数是下一步工作的主要目标。 参考文献： ZADEH L A. Toward a theory of fuzzy information granu￾lation and its centrality in human reasoning and fuzzy lo￾gic[J]. Fuzzy sets and systems, 1997, 90(2): 111–127. [1] PEDRYCZ W, SKOWRON A, KREINOVICH V. Hand￾book of granular computing[M]. Chichester: John Wiley & Sons, 2008: 719−740. [2] PEDRYCZ W, AL-HMOUZ R, MORFEQ A, et al. The design of free structure granular mappings: the use of the principle of justifiable granularity[J]. IEEE transactions on cybernetics, 2013, 43(6): 2105–2113. [3] WANG Guoyin, YANG Jie, XU Ji. Granular computing: from granularity optimization to multi-granularity joint problem solving[J]. Granular computing, 2017, 2(3): 105–120. [4] YAO Yiyu. Perspectives of granular computing[C]//Pro￾ceedings of 2015 IEEE International Conference on Granu￾lar Computing. Beijing, China, 2005: 85−90. [5] ZADEH L A. Fuzzy sets[J]. Information and control, 1965, 8(3): 338–353. [6] PAWLAK Z. Rough sets[J]. International journal of com￾puter & information sciences, 1982, 11(5): 341–356. [7] 张钹, 张铃. 问题求解理论及应用 [M]. 北京: 清华大学出 版社, 1990. [8] 李德毅, 孟海军, 史雪梅. 隶属云和隶属云发生器 [J]. 计 算机研究与发展, 1995(6): 15–20. LI Deyi, MENG Haijun, SHI Xuemei. Membership clouds and membership cloud generators[J]. Journal of computer research and development, 1995(6): 15–20. [9] 苗夺谦, 李德毅, 姚一豫, 等. 不确定性与粒计算 [M]. 北 京: 科学出版社, 2011. [10] [11] 徐计, 王国胤, 于洪. 基于粒计算的大数据处理 [J]. 计算 机学报, 2015(8): 1497–1517. XU Ji, WANG Guoyin, YU Hong. Review of big data processing based on granular computing[J]. Chinese journal of computers, 2015(8): 1497–1517. YAO Yiyu. Three-way decisions with probabilistic rough sets[J]. Information sciences, 2010, 180(3): 341–353. [12] QIAN Yuhua, LIANG Jiye, YAO Yiyu, et al. MGRS: a multi-granulation rough set[J]. Information sciences, 2010, 180(6): 949–970. [13] QIAN Yuhua, LIANG Jiye, DANG Chuangyin. Incom￾plete multigranulation rough set[J]. IEEE transactions on systems, man, and cybernetics-part A: systems and hu￾mans, 2010, 40(2): 420–431. [14] QIAN Yuhua, CHENG Honghong, WANG Jieting, et al. Grouping granular structures in human granulation intelli￾gence[J]. Information sciences, 2017, 382-383: 150–169. [15] 张钹, 张铃. 问题求解理论及应用 [M]. 北京: 清华大学 出版社, 1990. [16] ZHANG Ling, ZHANG Bo. The structure analysis of fuzzy sets[J]. International journal of approximate reason￾ing, 2005, 40(1/2): 92–108. [17] ZHANG Ling, ZHANG Bo. Fuzzy reasoning model un￾der quotient space structure[J]. Information sciences, 2005, 173(4): 353–364. [18] WIERMAN M J. Measuring uncertainty in rough set the￾ory[J]. International journal of general systems, 1999, 28(4/5): 283–297. [19] LIANG Jiye, CHIN K S, DANG Chuangyin, et al. A new method for measuring uncertainty and fuzziness in rough set theory[J]. International journal of general systems, 2002, 31(4): 331–342. [20] YAO Yiyu, ZHAO Liquan. A measurement theory view on the granularity of partitions[J]. Information sciences, 2012, 213: 1–13. [21] LAWVERE F W. Metric spaces, generalized logic, and closed categories[J]. Rendiconti del seminario matem￾atico e fisico di milano, 1973, 43(1): 135–166. [22] RUBNER Y, GUIBAS L, TOMASI C. The earth mover's distance, multi-dimensional scaling, and color-based im￾age retrieval[C]//Proceedings of the ARPA Image Under￾standing Workshop. 1997: 661−668. [23] RUBNER Y, TOMASI C, GUIBAS L J. The earth mover's distance as a metric for image retrieval[J]. Inter￾national journal of computer vision, 2000, 40(2): 99–121. [24] 郭增晓, 米据生. 粗糙模糊集的模糊性度量 [J]. 模糊系 统与数学, 2005, 19(4): 135–140. [25] 第 1 期 杨洁，等：基于知识距离的粗糙粒结构的评价模型 ·173·