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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

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
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