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山东大学学报（理学版） ›› 2017, Vol. 52 ›› Issue (7): 30-36.doi: 10.6040/j.issn.1671-9352.4.2017.130

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多粒度模糊粗糙近似算子的信任结构与属性约简

胡谦1,米据生1,2,李磊军1,2   

  1. 1.河北师范大学数学与信息科学学院, 河北 石家庄 050024;2.河北省计算数学与应用重点实验室(河北师范大学), 河北 石家 050024
  • 收稿日期:2017-03-06 出版日期:2017-07-20 发布日期:2017-07-07
  • 作者简介:胡谦(1991— ), 男, 硕士研究生, 研究方向为粗糙集与粒计算. E-mail:15227193972@163.com
  • 基金资助:
    国家自然科学基金资助项目(61573127,61502144,61300121,61472463);河北省自然科学基金资助项目(A2014205157);河北省高校创新团队领军人才培育计划项目(LJRC022);河北省博士后择优资助科研项目(B2016003013);河北省高校自然科学基金资助项目(QN2016133);河北师范大学博士科学基金资助项目(L2015B01);河北省教育厅研究生创新项目(sj2015001);河北师范大学研究生创新项目资助

The fuzzy belief structure and attribute reduction based on multi-granulation fuzzy rough operators

HU Qian1, MI Ju-sheng1,2, LI Lei-jun1,2   

  1. 1. College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024, Hebei, China;
    2. Hebei Key Laboratory of Computational Mathematics and Applications(Hebei Normal University), Shijiazhuang 050024, Hebei, China
  • Received:2017-03-06 Online:2017-07-20 Published:2017-07-07

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摘要： 多粒度是近年来粗糙集领域研究的一个热点方向, 为使多粒度模型更适用于实际数据, 提高模型的可用性, 模糊思想被引入到多粒度粗糙集模型中。本文构建了基于模糊相似关系下的多粒度模糊粗糙集模型, 并建立了模糊信任结构。在该信任结构下根据多粒度模糊粗糙集的上、下近似构造信任函数与似然函数。研究多粒度模糊粗糙集在模糊等价关系下的属性约简, 并给出相关算法。

关键词: 似然函数, 信任函数, 模糊粗糙集, 属性约简, 多粒度

Abstract: Multi-granulation is a hot direction in rough set theory. To make multi-granulation model more applicable to practical data, and to improve the usability of the model, the fuzzy concept is employed in multi-granulation model. A multi-granulation fuzzy rough set model is constructed based on fuzzy similarity relation, and a fuzzy belief structure is established. The belief function and probability function are constructed based on the upper and lower approximations of the multi-granulation fuzzy rough set under the trust structure. An attribute reduction of multi-granulation fuzzy rough sets is explored under fuzzy equivalence relation, and a reduction algorithm is formulated.

Key words: multi-granulation, belief function, attribute reduction, rough fuzzy set, probability function

中图分类号: 

  • O236
[1] ZADEH L A. Fuzzy sets[J]. Information and Control, 1965, 8: 338-353.
[2] PAWLAK Z. Rough sets[J]. International Journal of Computer and Information Sciences, 1982, 11(5):341-356.
[3] PAWLAK Z. Rough sets: Theoretical aspects of reasoning about data[M]. Dordrecht: Kluwre Academic Publishers, 1991.
[4] DUBOIS D, PRADE H. Rough fuzzy sets and fuzzy rough sets[J]. International Journal of General Systems, 1990, 17:191-209.
[5] DUBOIS D, PRADE H. Twofold fuzzy sets and rough sets-some issues in knowledge representation[J]. Fuzzy Sets and Systems, 1987, 23:3-18.
[6] BARNETT J A. Computational methods for a mathematical theory of evidence[C] // Proceedings of the 7th International Joint Conference on Artificial Intelligence. Vancouver: William Kaufmann, 1981: 868-875.
[7] AMINRAVAN F, SADIQ R, HOORFAR M, et al. Evidential reasoning using extended fuzzy Dempster-Shafer theory for handing various facets of information deficiency[J].International Journal of Intelligent Symstems, 2011, 26(8):731-758.
[8] CHEN Yaohua, YAO Yiyu. A multiview approach for intelligent data analysis based on data operators[J]. Information Sciences, 2008, 178(1):1-20.
[9] 苗夺谦, 徐菲菲, 姚一豫, 等. 粒计算的集合论描述[J]. 计算机学报, 2012, 35(2): 351-363. MIAO Duoqian, XU Feifei, YAO Yiyu, et al. Set-theoretic formulation of granular computing[J]. Chinese Journal of Computers, 2012, 35(2):351-363.
[10] YAO Yiyu. Granular computing: past, present, and future[C]. International Conference on Rough Sets and Knowledge Technology. Berlin:Springer, 2008: 27-28.
[11] QIAN Yuhua, LIANG Jiye, YAO Yiyu, et al. MGRS: a multi-granulation rough set[J]. Information Sciences, 2010, 180:949-970.
[12] XU Weihua, WANG Qiaorong, ZHANG Xiantao. Multi-granulation fuzzy rough sets in a fuzzy tolerance approximation space[J]. International Journal of Fuzzy Systems, 2011, 13(4):246-259.
[13] LIN Guoping, QIAN Yuhua, LI Jinjin. NMGRS: neighborhood-based multigranulation rough sets[J]. International Journal of Approximate Reasoning, 2012, 53:1080-1093.
[14] XU Weihua, SUN Wenxin, ZHANG Xiaoyan, et al. Multiple granulation rough set approach to or dered information systems[J]. International Journal of General Systems, 2012, 41:475-501.
[15] TAN Anhui, WU Weizhi, LI Jinjin, et al. Evidence-theory-based numerical characterization of multigranulation rough sets in incomplete information systems[J]. Fuzzy Sets and Systems, 2016, 294:18-35.
[16] LI Jinhai, REN Yue, MEI Changlin, et al. A comparative study of multigranulation rough sets and concept lattices via rule acquisition[J]. Knowledge-Based Systems, 2016, 91:152-164.
[17] MORDESON J. Fuzzy Mathematics[M]. Berlin: Springer, 2001.
[18] MURALI V. Fuzzy equivalence relations[J]. Fuzzy Sets and Systems, 1989, 30(2):155-163.
[19] 张文修, 梁怡, 吴伟志. 信息系统与知识发现[M]. 北京: 科学出版社, 2003. ZHANG Wenxiu, LIANG Yi, WU Weizhi. Information systems and knowledge discovery[M]. Bei Jing: Science Press, 2003.
[20] DEMPETER A P. Upper and lower probabilities induced by a multivalued mapping[J]. The Annals of Mathematical Statistics, 1967, 38:325-339.
[21] XU Weihua, WANG Qiaorong, ZHANG Xiantao. Multi-granulation fuzzy rough sets in a fuzzy tolerance approximation space[J]. International Journal of Fuzzy Systems, 2011, 13(4):246-259.
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