Rough sets and topological spaces based on similarity

被引：0
|
作者：
E. A. Abo-Tabl
机构：
[1] Assiut University,Mathematics Department, Faculty of Science
[2] Qassim University,Mathematics Department, Faculty of Science and Arts, Al
来源：
International Journal of Machine Learning and Cybernetics | 2013年 / 4卷
关键词：
Lower and upper approximations; Similarity relations; Rough sets; Topological space; Continuous function;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Ordinary topology now has been used in many sub-fields of artificial intelligence, such as knowledge representation, spatial reasoning etc. In this paper, we discuss the relationships between the theory of rough sets and topological spaces. We obtain the concepts of rough sets from topology, also we obtain the concepts of topological space from rough sets. Furthermore, if the function between two topological spaces is bijective, open and continuous, then the image and the inverse image of a rough set are also rough.
引用
收藏
页码：451 / 458
页数：7
相关论文
共 50 条
  • [1] Rough sets and topological spaces based on similarity
    Abo-Tabl, E. A.
    INTERNATIONAL JOURNAL OF MACHINE LEARNING AND CYBERNETICS, 2013, 4 (05) : 451 - 458
  • [2] ON RELATIONSHIP BETWEEN MODIFIED SETS, TOPOLOGICAL-SPACES AND ROUGH SETS
    KORTELAINEN, J
    FUZZY SETS AND SYSTEMS, 1994, 61 (01) : 91 - 95
  • [3] Generalized soft rough sets and generated soft ideal rough topological spaces
    Abd El-Latif, A. M.
    JOURNAL OF INTELLIGENT & FUZZY SYSTEMS, 2018, 34 (01) : 517 - 524
  • [4] Topological space properties of rough sets
    Liu, WJ
    PROCEEDINGS OF THE 2004 INTERNATIONAL CONFERENCE ON MACHINE LEARNING AND CYBERNETICS, VOLS 1-7, 2004, : 2353 - 2355
  • [5] Rough Sets: A Topological View
    Kumar, Arun
    Kumari, Shilpi
    NEW MATHEMATICS AND NATURAL COMPUTATION, 2024,
  • [6] Topological Interpretation of Rough Sets
    Grabowski, Adam
    FORMALIZED MATHEMATICS, 2014, 22 (01): : 89 - 97
  • [7] A generalized definition of rough approximation based on similarity in variable precision rough sets
    Zhao, SX
    Zhang, ZR
    PROCEEDINGS OF 2005 INTERNATIONAL CONFERENCE ON MACHINE LEARNING AND CYBERNETICS, VOLS 1-9, 2005, : 3153 - 3156
  • [8] On structures of rough topological spaces based on neighborhood systems
    Abu-Gdairi, Radwan
    ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2023, (50): : 61 - 74
  • [9] Some topological properties of rough approximation spaces
    Liu, Wei-Jiang
    Bai, Lei
    Jing, Quan
    PROCEEDINGS OF 2006 INTERNATIONAL CONFERENCE ON MACHINE LEARNING AND CYBERNETICS, VOLS 1-7, 2006, : 2305 - +
  • [10] SIMILARITY MEASURES OF FUZZY ROUGH SETS BASED ON THE LP METRIC
    Ye, Qi-Hong
    Wu, Wei-Zhi
    PROCEEDINGS OF 2009 INTERNATIONAL CONFERENCE ON MACHINE LEARNING AND CYBERNETICS, VOLS 1-6, 2009, : 811 - 816
12345