您的位置：山东大学 -> 科技期刊社 -> 《山东大学学报（理学版）》

《山东大学学报(理学版)》 ›› 2026, Vol. 61 ›› Issue (1): 85-93.doi: 10.6040/j.issn.1671-9352.0.2024.035

• • 上一篇    

基于二型模糊预序的模糊粗糙集模型

张光旭1,姚卫2   

  1. 1.南京工程学院数理学院, 江苏 南京 211167;2.南京信息工程大学数学与统计学院, 江苏 南京 210044
  • 发布日期:2026-01-15
  • 作者简介:张光旭(1995— ),女,讲师,博士,研究方向为模糊集理论及应用. E-mail:hbgxzhang@163.com
  • 基金资助:
    国家自然科学基金资助项目(12371462,12231007);南京工程学院引进人才科研启动基金资助项目(YKJ202351);江苏省双创人才计划(JSSCRC2021521);黑龙江省自然科学基金联合基金重点项目(ZL2024A001)

Fuzzy rough set model based on type-2 fuzzy preorders

ZHANG Guangxu1, YAO Wei2   

  1. 1. School of Mathematics and Physics, Nanjing Institute of Technology, Nanjing 211167, Jiangsu, China;
    2. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, Jiangsu, China
  • Published:2026-01-15

PDF (PC)

4

摘要： 以二型模糊预序为基本结构研究了模糊粗糙集,定义一对模糊上下近似算子,并研究它们的性质和相互关系,证明上可定义集和下可定义集是等价的,上可定义集和下可定义集构成一个满层的Alexandrov模糊拓扑。

关键词: 二型模糊预序, 模糊粗糙集, 模糊近似算子, 可定义集, Alexandrov模糊拓扑

Abstract: Based on the fundamental structure of type-2 fuzzy preorders, fuzzy rough sets are investigated, and a pair of fuzzy upper and lower approximation operators are defined. Furthermore, their properties and interrelations are explored. It is shown that upper definable sets and lower definable sets are equivalent. Definable sets form a stratified Alexandrov fuzzy topology such that the upper and lower approximation operators are the related closure and interior operators respectively.

Key words: type-2 fuzzy preorder, fuzzy rough set, fuzzy upper/lower approximation operator, definable set, Alexandrov fuzzy topology

中图分类号: 

  • O181
[1] PAWLAK Z. Rough sets[J]. International Journal of Computer and Information Sciences, 1982, 11(5):341-356.
[2] BELOHLAVEK R. Fuzzy relational systems: foundations and principles[M]. New York: Kluwer Academic Publishers, 2002: 1-5.
[3] 刘清,黄兆华,刘少辉,等. 带Rough算子的决策规则及数据挖掘中的软计算[J]. 计算机研究与发展,1999,36:800-804. LIU Qing, HUANG Zhaohua, LIU Shaohui, et al. Decision rules with rough operator and soft computing of data mining[J]. Journal of Computer Research and Development, 1999, 36:800-804.
[4] CIUCCI D E, CATTANEO G. Algebraic structures for rough sets[J]. Transactions on Rough Sets II, 2004, 3135:208-252.
[5] SKOWRON A, STEPANIUK J. Tolerance approximation spaces[J]. Fundamenta Informaticae, 1996, 27(2/3):245-253.
[6] SLOWINSKI R, VANDERPOOTEN D. A generalized definition of rough approximations based onsimilarity[J]. IEEE Transactions on Knowledge and Data Engineering, 2000, 12(2):331-336.
[7] BONIKOWSKI Z, BRYNIARSKI E, WYBRANIEC-SKARDOWSKA U. Extensions and intentions in the rough settheory[J]. Information Sciences, 1998, 107(1/4):149-167.
[8] ZAKOWSKI W. Approximations in the space(u,p)[J]. Demonstratio Mathematica, 1983, 16(3):761-769.
[9] 米据生,吴伟志,张文修. 粗糙集的构造与公理化方法[J]. 模式识别与人工智能,2002,15(3):280-284. MI Jusheng, WU Weizhi, ZHANG Wenxiu. Constructive and axiomatic approaches of the theory of rough sets[J]. Pattern Recognition and Artificial Intelligence, 2002, 15(3):280-284.
[10] DUBOIS D, PRADE H. Rough fuzzy sets and fuzzy roughsets[J]. International Journal of General Systems, 1990, 17(2/3):191-209.
[11] LIU Guilong. The axiomatization of the rough set upper approximation operations[J]. Fundamenta Informaticae, 2006, 69(3):331-342.
[12] WU Weizhi, MI Jusheng, ZHANG Wenxiu. Generalized fuzzy rough sets[J]. Information Sciences, 2003, 151:263-282.
[13] RADZIKOWSKA A M. On lattice-based fuzzy rough sets[M] //CORNELIS C G, DESCHRIJVER M, NACHTEGAEL S, et al. Years of Fuzzy Set Theory. Berlin: Springer, 2010:107-126.
[14] RADZIKOWSKA A M, KERRE EE. Fuzzy rough sets based on residuated lattices[J]. Lecture Notes in Computer Science, 2005, 3135:278-296.
[15] SHE Yanhong, WANG Guojun. An axiomatic approach of fuzzy rough sets based on residuated lattices[J]. Computers and Mathematics with Applications, 2009, 58(1):189-201.
[16] DENG Tingquan, CHEN Yanmei, XU Wenli, et al. A novel approach to fuzzy rough sets based on a fuzzy covering[J]. Information Sciences, 2007, 177(11):2308-2326.
[17] FENG Tao, ZHANG Shaopu, MI Jusheng. The reduction and fusion of fuzzy covering systems based on the evidence theory[J]. International Journal of Approximate Reasoning, 2012, 53(1):87-103.
[18] LI T J, LEUNG Y, ZHANG W X. Generalized fuzzy rough approximation operators based on fuzzy coverings[J]. International Journal of Approximate Reasoning, 2008, 48(3):836-856.
[19] DEER L, CORNELIS C, GODO L. Fuzzy neighborhood operators based on fuzzy coverings[J]. Fuzzy Sets and Systems, 2017, 312:17-35.
[20] YAO Wei, SHE Yanhong, LU Lingxia. Metric-based L-fuzzy rough sets: approximation operators and definable sets[J]. Knowledge-Based Systems, 2019, 163:91-102.
[21] YAO Wei, ZHANG Guangxu, ZHOU Changjie. Real-valued hemimetric-based fuzzy rough sets and an application to contour extraction of digital surfaces[J]. Fuzzy Sets and Systems, 2023, 459:201-219.
[22] GOUBAULT-LARRECQ J. Non-Hausdorff topology and domain theory[M]. Cambridge: Cambridge University Press, 2013: 1-10.
[23] ZADEH L A. Similarity relations and fuzzy orderings[J]. Information Sciences, 1971, 3(2):177-200.
[24] YAO Wei, ZHANG Guangxu, SHI Yi. Type-2 lattice-valued preorders: a common framework of lattice-valued preorders and various kinds of metrics[J]. Iranian Journal of Fuzzy Systems, 2023, 20(3):191-203.
[25] ZHANG Guangxu, YAO Wei. Fuzzy rough sets based on modular hemimetrics[J]. Soft Computing, 2023, 27:4393-4401.
[26] ZHANG Guangxu, YAO Wei. Fuzzy rough sets based on Morsi fuzzy hemimetrics[J]. Hacettepe Journal of Mathematics and Statistics, 2024, 53(1):107-120.
[27] 杨俊. 基于乘除法的模糊预序型模糊粗糙集[D]. 南京:南京信息工程大学,2023. YANG Jun. Fuzzy preorder based fuzzy rough sets using multiplication and division[D]. Nanjing: Nanjing University of Information Science and Technology, 2023.
[28] KLEMENT E P, MESIAR R, PAP E. Triangular norms[M]. Dordrecht: Kluwer Academic Publishers, 2000.
[29] 张小红,裴道武,代建华. 模糊数学与Rough集理论[M]. 北京:清华大学出版社,2013:116. ZHANG Xiaohong, PEI Daowu, DAI Jianhua. Fuzzy mathematics and rough sets theroy[M]. Beijing: Tsinghua University Press, 2013:116.
[30] DEER L, CORNELIS C, YAO Y Y. A semantically sound approach to Pawlak rough sets and covering-based rough sets[J]. International Journal of Approximate Reasoning, 2016, 78(11):62-72.
[31] RALEVIC N M, KARAKLIC D, PIŠTINJAT N. Fuzzy metric and its applications in removing the imagenoise[J]. Soft Computing, 2019, 23(22):12049-12061.
[1] 李文焱,李丽红,王洪欣. 基于知识度量的模糊粗糙c-均值算法[J]. 《山东大学学报(理学版)》, 2026, 61(1): 49-64.
[2] 李心如,李令强,贾成昭. 新型多粒度变精度(*,·)-模糊粗糙集[J]. 《山东大学学报(理学版)》, 2025, 60(7): 131-142.
[3] 吴凡,孔祥智. 基于模糊信息系统的模糊β-覆盖粗糙集模型[J]. 《山东大学学报(理学版)》, 2023, 58(5): 10-16.
[4] 熊兴国,路玲霞. 基于MV-代数的度量型模糊粗糙集[J]. 《山东大学学报(理学版)》, 2019, 54(11): 81-89.
[5] 胡谦,米据生,李磊军. 多粒度模糊粗糙近似算子的信任结构与属性约简[J]. 山东大学学报（理学版）, 2017, 52(7): 30-36.
[6] 罗海燕, 吕萍, 刘林忠, 杨洵. 云环境下基于模糊粗糙AHP的企业信任综合评估[J]. 山东大学学报（理学版）, 2014, 49(08): 111-117.
[7] 鲁小云1,杨勇2. 单向S-模糊粗糙集及其应用[J]. J4, 2011, 46(8): 110-113.
[8] 林梦雷1,杨伟萍2. 蕴涵区间直觉模糊粗糙集及其性质[J]. J4, 2011, 46(8): 104-109.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
版权所有 © 2018 《山东大学学报(理学版)》编辑部　
地址: 山东省济南市山大南路27号山东大学中心校区（250100）　电话: +86-0531-88366917　E-mail: xblxb@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