Rough ideals in lattices

被引:10
|
作者
Xiao, Qimei [1 ,2 ]
Li, Qingguo [1 ]
Zhou, Xiangnan [1 ]
机构
[1] Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China
[2] Changsha Univ Sci & Technol, Sch Math & Comp Sci, Changsha 410004, Hunan, Peoples R China
来源
基金
美国国家科学基金会;
关键词
Rough set; Lattice; Rough ideals; Homomorphism; UPPER APPROXIMATIONS; ALGEBRAIC STRUCTURES; SETS; SYSTEMS; RINGS;
D O I
10.1007/s00521-011-0801-5
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
In this paper, we consider a relationship between rough sets and lattice theory. The related properties of rough subsets of lattices are investigated. We introduce the notion of rough ideals which is a generalized notion of ideals of a lattice, and some properties and homomorphism of such ideals are discussed.
引用
收藏
页码:S245 / S253
页数:9
相关论文
共 50 条
  • [1] Rough ideals in lattices
    Qimei Xiao
    Qingguo Li
    Xiangnan Zhou
    Neural Computing and Applications, 2012, 21 : 245 - 253
  • [2] Rough sets induced by ideals in lattices
    Xiao, Qimei
    Li, Qingguo
    Guo, Lankun
    INFORMATION SCIENCES, 2014, 271 : 82 - 92
  • [3] A new approach to rough lattices and rough fuzzy lattices based on fuzzy ideals
    Zhu, Kuanyun
    Wang, Jingru
    Yang, Yongwei
    IAENG International Journal of Applied Mathematics, 2019, 49 (04): : 1 - 7
  • [4] Rough sets induced by ideals in skew lattices
    Zhi, Yuan
    Zhou, Xiangnan
    Li, Qingguo
    JOURNAL OF INTELLIGENT & FUZZY SYSTEMS, 2017, 33 (06) : 3913 - 3928
  • [5] A new study on rough soft lattices based on ideals
    Zhu, Kuanyun
    Wang, Jingru
    ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2021, Forum-Editrice Universitaria Udinese SRL (45): : 590 - 599
  • [6] Rough sets based on fuzzy ideals in distributive lattices
    Yang, Yongwei
    Zhu, Kuanyun
    Xin, Xiaolong
    OPEN MATHEMATICS, 2020, 18 : 122 - 137
  • [7] A new study on soft rough fuzzy lattices (ideals, filters) over lattices
    Zhu, Kuan Yun
    Hu, Bao Qing
    JOURNAL OF INTELLIGENT & FUZZY SYSTEMS, 2017, 33 (04) : 2391 - 2402
  • [8] On ⊙-Ideals and Lattices of ⊙-Ideals in Regular Residuated Lattices
    Liu, Chun-hui
    Xu, Luo-shan
    QUANTITATIVE LOGIC AND SOFT COMPUTING 2010, VOL 2, 2010, 82 : 425 - 434
  • [9] EMBEDDING LATTICES INTO LATTICES OF IDEALS
    GRATZER, G
    PLATT, CR
    SANDS, B
    PACIFIC JOURNAL OF MATHEMATICS, 1979, 85 (01) : 65 - 75
  • [10] On Rough Ideals and Rough Fuzzy Ideals of BCI-algebras
    Chen, Lu
    Wang, Feng-xiao
    FIFTH INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS AND KNOWLEDGE DISCOVERY, VOL 5, PROCEEDINGS, 2008, : 281 - 284