您的位置：山东大学 -> 科技期刊社 -> 《山东大学学报（工学版）》

山东大学学报 (工学版) ›› 2022, Vol. 57 ›› Issue (5): 1-10.doi: 10.6040/j.issn.1671-9352.4.2021.250

• •    

基于Bayesian直觉模糊粗糙集的数据分类方法

薛占熬1,2*,李永祥1,2,姚守倩1,2,荆萌萌1,2   

  1. 1.河南师范大学计算机与信息工程学院, 河南 新乡 453007;2.智慧商务与物联网技术河南省工程实验室, 河南 新乡 453007
  • 发布日期:2022-06-21
  • 作者简介:薛占熬(1963— ),男,教授,博士,研究方向为人工智能基础理论、粗糙集理论和三支决策理论. E-mail:xuezhanao@163.com*通信作者
  • 基金资助:
    国家自然科学基金资助项目(62076089,61772176);河南省科技攻关项目(182102210078,212102210136)

Data classification method based on Bayesian intuitionistic fuzzy rough sets

XUE Zhan-ao1,2*, LI Yong-xiang1,2, YAO Shou-qian1,2, JING Meng-meng1,2   

  1. 1. College of Computer and Information Engineering, Henan Normal University, Xinxiang 453007, Henan, China;
    2. Engineering Lab of Intelligence Business &
    Internet of Things, Henan Province, Xinxiang 453007, Henan, China
  • Published:2022-06-21

PDF (PC)

48

摘要： 在直觉模糊集和粗糙集理论基础上,结合Bayesian概率和近似关系,提出了Bayesian直觉模糊粗糙集模型,并对其进行研究。首先,在粗糙集的基础上,定义了基于直觉模糊粗糙集上的Bayesian概率,结合直觉模糊近似关系和模糊矩阵,给出了直觉模糊等价关系,并讨论了其性质;其次,根据直觉模糊集和截集的特性,得到基于Bayesian直觉模糊粗糙集的等价类,并进一步给出了上、下近似的划分方法,求出正、负域和边界域并计算近似精度;最后,在UCI数据集上,分析验证该模型的有效性,该模型能较好地分类含有模糊信息的数据。

关键词: Bayesian粗糙集, 直觉模糊集, 直觉模糊等价关系, 近似精度, 数据分类

Abstract: This paper proposed a Bayesian intuitionistic fuzzy rough set model based on the theory of intuitionistic fuzzy sets and rough sets, Bayesian probability and approximate relations is combined, and conducted research on it. Firstly, on the basis of rough sets, Bayesian probability based on intuitionistic fuzzy rough set is defined, combined with intuitionistic fuzzy approximation relation and fuzzy matrix, the intuitionistic fuzzy equivalence relation is given, and its properties are discussed. Secondly, according to the characteristics of intuitionistic fuzzy sets and cut sets, the equivalence class basis of Bayesian intuitionistic fuzzy rough sets is obtained, and the upper and lower approximation division method are further given, the positive, negative and boundary fields are calculated and the approximate accuracy is calculated. Finally, the effectiveness of the model is analyzed and verified, and the data with fuzzy information can be better classified on the UCI data sets.

Key words: Bayesian rough set, intuitionistic fuzzy set, intuitionistic fuzzy equivalence relation, approximate accuracy, data classification

中图分类号: 

  • TP391
[1] PAWLAK Z. Rough sets[J]. International Journal of Computer and Information Sciences, 1982, 11(5):341-356.
[2] ZIARKO W. Variable precision rough set model[J]. Journal of Computer and System Science, 1993, 46(1):39-59.
[3] ZHAO S Y, TSANG E C C, CHEN D G. The model of fuzzy variable precision rough sets[J]. IEEE Transactions on Fuzzy Systems, 2009, 17(2):451-467.
[4] SUN Bingzhen, MA Weimin. Fuzzy rough set model on two different universes and its application[J]. Applied Mathematical Modelling, 2011, 35(4):1798-1809.
[5] WANG Chunyong. A comparative study of variable precision fuzzy rough sets based on residuated lattices[J]. Fuzzy Sets and Systems, 2019, 37(3):94-115.
[6] LI Juan, SHAO Yabin, QI Xiaoding. On variable-precision-based rough set approach to incomplete interval-valued fuzzy information systems and its applications[J]. Journal of Intelligent and Fuzzy Systems, 2020(1):1-12.
[7] ZIARKO W. Variable precision rough set model[J]. Journal of Computer and System Science, 1993, 46(1):39-59.
[8] YAO Y Y. Decision-theoretic rough set models[M] //Rough Sets and Knowledge Technology. Toronto: Springer, 2007: 1-12.
[9] 薛占熬,张敏,赵丽平,等.集对优势关系下多粒度决策粗糙集的可变三支决策模型[J].计算机科学,2021,48(1):157-166. XUE Zhanao, ZHANG Min, ZHAO Liping, et al. Variable three-way decision model of multi-granulation decision rough sets under set-pair dominance relation[J]. Computer Science, 2021, 48(1):157-166.
[10] 薛占熬,韩丹杰,吕敏杰,等.一种新的基于粒度重要度的三支决策模型[J].计算机科学,2019,46(2):236-241. XUE Zhanao, HAN Danjie, LYU Minjie, et al. New three-way decisions model based on granularity importance degree[J]. Computer Science, 2019, 46(2):236-241.
[11] 徐久成,徐战威,李梦凡,等.基于三支决策的二阶段分类模型研究[J].河南师范大学学报(自然科学版),2019,47(3):28-34,124. XU Jiucheng, XU Zhanwei, LI Mengfan, et al. Research on two-stage classification model based on three-way decisions[J]. Journal of Henan Normal University(Natural Science Edition), 2019, 47(3):28-34,124.
[12] PAWLAK Z. Decision rules, Bayes rule and rough sets[J]. Lecture Notes in Computer Science, 1999, 3(2):1-9.
[13] 韩敏,张俊杰,彭飞,等.一种基于多决策类的贝叶斯粗糙集模型[J].控制与决策,2009,24(11):1615-1619. HAN Min, ZHANG Junjie, PENG Fei, et al. Bayesian rough set model based on multiple decision classes[J]. Control and Decision, 2009, 24(11):1615-1619.
[14] 胡名彩,郭伏,叶国全.基于改进变精度贝叶斯粗糙集的感性知识获取[J].东北大学学报(自然科学版),2018,39(12):1794-1799. HU Mingcai, GUO Fu, YE Guoquan. Kansei knowledge acquisition based on the improved variable precision Bayesian rough set[J]. Journal of Northeastern University(Natural Science), 2018, 39(12):1794-1799.
[15] ZHANG Hongyun, ZHOU Jie, MIAO Duoqian, et al. Bayesian rough set model:a further investigation[J]. International Journal of Approximate Reasoning, 2012, 53(4):541-557.
[16] 卓德强.基于贝叶斯粗糙集的肺部肿瘤CT图像抗噪算法设计[J].生物医学工程研究,2019,38(3):331-335. ZHUO Deqiang. Design of noise control algorithm for CT image of pulmonary tumor based on Bayesian rough set[J]. Journal of Biomedical Engineering Research, 2019, 38(3):331-335.
[17] ZADEH L A. Fuzzy sets[J]. Information and Control, 1965(8):338-353.
[18] ZADEH L A. A note on prototype theory and fuzzy sets[J]. Cognition, 1982, 12(3):291-297.
[19] ATANASSOV K T. Intuitionistic fuzzy sets[J]. Fuzzy Sets and Systems, 1986, 20(1):87-96.
[20] TORRA V. Hesitant fuzzy sets[J]. International Journal of Intelligent Systems, 2010, 25(6):529-539.
[21] TORRA V, NARUKAWA Y. On hesitant fuzzy sets and decision[C] //2009 IEEE International Conference on Fuzzy Systems. Piscataway: IEEE, 2009: 1378-1382.
[22] 胡晓元,孙秉珍.基于双论域量化模糊粗糙集的公共卫生应急决策模型[J].系统科学与数学,2019,39(3):409-424. HU Xiaoyuan, SUN Bingzhen. The model of public health emergency decision-making based on double quantitative fuzzy rough set over two universes[J]. Journal of Systems Science and Mathematical Sciences, 2019, 39(3):409-424.
[23] 刘丹,李敬伟.基于矩阵的双论域模糊概率粗糙集增量更新算法[J].控制与决策,2021,36(3):553-564. LIU Dan, LI Jingwei. Incremental updating of fuzzy probability rough sets over two universes based on matrix method[J]. Control and Decision, 2021, 36(3):553-564.
[24] 张晶,李德玉,王素格,等.基于稳健模糊粗糙集模型的多标记文本分类[J].计算机科学,2015,42(7):270-275. ZHANG Jing, LI Deyu, WANG Suge, et al. Multi-label text classification based on robust fuzzy rough set model[J]. Computer Science, 2015, 42(7):270-275.
[25] 李亚鸽,杨宏志,徐久成.基于不完备信息系统的三角模糊数决策粗糙集[J].智能系统学报,2016,11(4):449-458. LI Yage, YANG Hongzhi, XU Jiucheng. Triangular fuzzy number decision-theoretic rough sets under incomplete information systems[J]. CAAI Transactions of Intelligent Systems, 2016, 11(4):449-458.
[26] YANG Hailong, LIAO Xiuwu, WANG Shouyang, et al. Fuzzy probabilistic rough set model on two universes and its applications[J]. International Journal of Approximate Reasoning, 2013, 54(9):1410-1420.
[27] 谈静.犹豫模糊有序信息系统的属性约简[D].成都:西华大学,2019. TAN Jing. Hesitant fuzzy attribute reduction of ordered information system[D]. Chengdu: Xihua University, 2019.
[28] CHEN Yingyue, CHEN Yumin. Feature subset selection based on variable precision neighborhood rough sets[J]. International Journal of Computational Intelligence Systems, 2021, 14(1):572-581.
[29] 张利亭,冯涛,李欢.不完备信息系统的直觉模糊决策粗糙集[J].郑州大学学报(理学版),2021,53(2):57-65. ZHANG Liting, FENG Tao, LI Huan. Intuitionistic fuzzy decision rough sets for incomplete information systems[J]. Journal of Zhengzhou University(Natural Science Edition), 2021, 53(2):57-65.
[30] YAO Y Y, ZHOU B. Two Bayesian approaches to rough sets[J]. European Journal of Operational Research, 2016, 251(3):904-917.
[1] 曹雅,邓赵红,王士同. 基于单调约束的径向基函数神经网络模型[J]. 山东大学学报(工学版), 2018, 48(3): 127-133.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
版权所有 © 2018 《山东大学学报(工学版)》编辑部　
地址: 济南市山大南路27号（250100）　 电话: 0531-88366735　 E-mail: xbgxb@sdu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发