计算机科学 ›› 2021, Vol. 48 ›› Issue (4): 49-53.doi: 10.11896/jsjkx.200900089

• 计算机科学理论 • 上一篇    下一篇

三种近似算子之间的关系

鲁巡, 李妍妍, 秦克云   

  1. 西南交通大学数学学院 成都 611756
  • 收稿日期:2020-06-24 修回日期:2020-11-09 出版日期:2021-04-15 发布日期:2021-04-09
  • 通讯作者: 秦克云(keyunqin@263.net)
  • 基金资助:
    国家自然科学基金项目(61976130,61473239)

Relationship Among Three Types of Rough Approximation Pairs

LU Xun, LI Yan-yan, QIN Ke-yun   

  1. College of Mathematic,Southwest Jiaotong University,Chengdu 611756,China
  • Received:2020-06-24 Revised:2020-11-09 Online:2021-04-15 Published:2021-04-09
  • About author:LU XUN,born in 1995,postgraduate.His main research interests include rough set theory,formal concept analysis and so on.(2900501866@qq.com)
    QIN Ke-yun,born in 1962,Ph.D,professor,Ph.D supervisor.His main research interests include rough set theory,formal concept analysis and so on.
  • Supported by:
    National Natural Science Foundation of China(61976130,61473239).

摘要: 在广义近似空间中,可以从对象、知识粒以及子系统的角度构造3种不同类型的广义粗糙近似算子。文中研究了这些近似算子的基本性质与相互关系,给出了3类近似算子相同的充要条件。另外,不同的近似空间可能生成相同的基于知识粒及基于子系统的近似算子,文中给出了不同二元关系生成相同近似算子的一些充要条件。

关键词: 广义近似空间, 近似算子, 左、右邻域

Abstract: In generalized approximation spaces,approximation operators can be constructed based on elements,knowledge gra-nules and subsystems.This paper is devoted to discussion of basic properties and relationships among these three types of approximation operators.Some necessary and sufficient conditions for approximation operators coincide with each other are provi-ded.In addition,different approximation spaces may generate same granule based or subsystem based rough approximation operators.Some necessary and sufficient conditions for different approximation spaces generating same approximate operators are surveyed.

Key words: Approximation operator, Generalized approximation space, Left and right relative sets

中图分类号: 

  • TP182
[1]PAWLAK Z.Rough sets[J].International Journal of Computer &Information Sciences,1982,11(5):341-356.
[2]DAI J,XU Q.Approximations and uncertainty measures in incomplete information systems[J].Information Sciences,2012,198(1):62-80.
[3]KANEIWA K,KUDO Y.A sequential pattern mining algorithm using rough set theory [J].International Journal of Approximate Reasoning,2011,52(6):881-893.
[4]YAO Y Y,ZHOU B.Two Bayesian approaches to rough sets [J].European Journal of Operational Research,2016,251:904-917.
[5]YAO Y Y.Three-way decision with probabilistic rough sets[J].Information Sciences,2010,180(3):341-353.
[6]YAO Y Y.Relational interpretations of neighbor-hood operators and rough set approximation operators[J].Information Scie-nces,1998,111(1):239-259.
[7]YAO Y Y.Constructive and algebraic methods of rough sets[J].Information Sciences,1998,109(1):21-47.
[8]SLOWINSKI R,VANDERPOOTEN D.A generalized definition of rough approximations based on similarity [J].IEEE Transactions on Knowledge and Data Engineering,2000,12:331-336.
[9]DUBOIS D,PRADE H.Rough fuzzy sets and fuzzy rough sets [J].International Journal of General Systems,1990,17:191-209.
[10]RADZIKOWSKA A M,KERRE E E.A comparative study offuzzy rough sets [J].Fuzzy Sets and Systems,2002,126:137-155.
[11]MI J S,LEUNG Y,ZHAO H Y,et al.Generalized fuzzy rough sets determined by a triangular norm [J].Information Sciences,2008,178:3203-3213.
[12]BONIKOWSKI Z,BRYNIARSKI E,WYBRANIEC-SKARDO-WSKA U.Extensions and intentions in the rough set theory [J].Information Sciences,1998,107:149-167.
[13]ZHU W,WANG F Y.On three types of covering based rough sets [J].IEEE Transactions on Knowledge and Data Enginee-ring,2007,19(8):1131-1144.
[14]KONDO M.On the structure of generalized rough sets [J].Information Sciences,2006,176(5):589-600.
[15]QIN K Y,YANG J L,PEI Z.Generalized rough sets based on reflexive and transitive relations [J].Information Sciences,2008,178(21):4138-4141.
[16]QIN K Y,PEI Z.On the topological properties of fuzzy rough sets [J].Fuzzy Sets and Systems,2005,151:601-613.
[17]LASHIN E F,KOZAE A M,MEDHHAT T,et al.Rough set theory for topological spaces [J].International Journal of Approximate Reasoning,2005,49(1/2):35-43.
[18]ZHU W.Topological approaches to covering rough sets [J].Information Sciences,2007,177:1499-1508.
[19]ZHANG Y L,LI C Q.Topological structures of a type of gra-nule based covering rough sets [J].Filomat,2018,32(9):3129-3141.
[20]WU H S,LIU G L.The relationships between topologies andgeneralized rough sets[J].International Journal of Approximate Reasoning,2020,119:313-324.
[21]ZHANG W X,WU W Z,LIANG J Y,et al.Rough set theory and method[M].Beijing:Science Press,2001.
[22]LIU G L.A comparison of two types of generalized rough sets[C]//IEEE International Conference on Granular Computing.IEEE Computer Society,2012:423-426.
[23]LIU G L,ZHU K.The relationship among three types of rough approximation pairs [J].Knowledge-Based Systems,2014,60:28-34.
[24]ZHANG Y L,LI C Q.Topological properties of a pair of relation based approximation operators [J].Filomat,2017,31(19):6175-6183.
[25]AKOWSKI W.Approximations in the space (u,π)[J].Demonstration Mathematics,1983,16(3):761-769.
[26]ZHU W.Relationship between generalized rough sets based on binary relation and covering [J].Information Sciences,2009,179(1):210-225.
[27]BOUZAYANE S,SAAD L.A multicriteria approach based on rough set theory for the incremental Periodic prediction [J].European Journal of Operational Research,2020,286(1):282-298.
[1] 许思雨, 秦克云.
基于剩余格的模糊粗糙集的拓扑性质
Topological Properties of Fuzzy Rough Sets Based on Residuated Lattices
计算机科学, 2022, 49(6A): 140-143. https://doi.org/10.11896/jsjkx.210200123
[2] 李妍妍, 秦克云.
广义粗糙近似算子的拓扑性质
On Topological Properties of Generalized Rough Approximation Operators
计算机科学, 2022, 49(3): 263-268. https://doi.org/10.11896/jsjkx.210100204
[3] 孔庆钊,韦增欣.
多粒化的模糊粗糙集代数
Fuzzy Rough Set Algebra of Multi-granulation
计算机科学, 2016, 43(4): 206-209. https://doi.org/10.11896/j.issn.1002-137X.2016.04.042
[4] 孔庆钊,韦增欣.
多粒化的粗糙集代数
Rough Set Algebra of Multi-granulation
计算机科学, 2016, 43(2): 68-71. https://doi.org/10.11896/j.issn.1002-137X.2016.02.015
[5] 李长清,张燕兰.
一类覆盖近似算子的动态更新方法
Updating Approximations for a Type of Covering-based Rough Sets
计算机科学, 2016, 43(1): 73-76. https://doi.org/10.11896/j.issn.1002-137X.2016.01.017
[6] 秦克云,罗珺方.
基于程度不可区分关系的粗糙集模型
Rough Set Model Based on Grade Indiscernibility Relation
计算机科学, 2015, 42(8): 240-243.
[7] 孙峰,王敬前.
覆盖粗糙集的图表示和2-部矩阵
Graph Representation and 2-part Matrix of Covering-based Rough Sets
计算机科学, 2014, 41(3): 85-87.
[8] 薛占熬,程惠茹,黄海松,肖运花.
模糊空间中的直觉模糊粗糙近似
Rough Approximations of Intuitions Fuzzy Sets in Fuzzy Approximation Space
计算机科学, 2013, 40(4): 221-226.
[9] 赵涛,秦克云.
基于分子格的粗糙集模型推广
Generalization of Rough Set Model Based on Molecular Lattices
计算机科学, 2012, 39(2): 258-261.
[10] 梁俊奇,闰淑霞.
关于覆盖粗糙集模型性质的一个注记
Note of Covering Rough Set Model Nature
计算机科学, 2011, 38(9): 234-236.
[11] 梁俊奇,张文君.
变精度覆盖近似算子与覆盖近似算子的关系
Relations between for Variable Precision Covering Approximation Operators and Covering Approximation Operators
计算机科学, 2011, 38(3): 222-223.
[12] 乔全喜,秦克云.
无限论域上粗糙集的拓扑结构
Topological Structure of Rou沙 Sets in Infinite Universes
计算机科学, 2011, 38(10): 228-230.
[13] 徐优红.
二元关系的复合与近似算子的合成

计算机科学, 2009, 36(2): 194-198.
[14] .
广义区间值模糊粗糙近似算子的构造研究

计算机科学, 2009, 36(1): 158-161.
[15] .
粗糙集近似与信息粒度

计算机科学, 2008, 35(3): 222-224.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!