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粗糙集的拓扑结构 被引量:12

On Topological Structure of Rough Sets
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摘要 本文在Pawlak近似空间意义下研究粗糙集构成的拓扑空间。借助粗糙集的表示构造了粗糙拓扑空间,其中的开集为粗糙相等关系下的等价类;讨论了粗糙拓扑空间中的内部、闭包算子与近似空间中粗糙近似算子的关系,并给出了粗糙拓扑空间的拓扑基。 This paper is devoted to the discussion of topological structure of rough sets in Pawlak approximation space. The rough topological space is constructed based on the representation of rough sets. The relationship among interior operator, closure operator and rough approximation operators is investigated and the base of rough topological space is given.
出处 《计算机科学》 CSCD 北大核心 2007年第12期161-162,241,共3页 Computer Science
基金 国家自然科学基金资助项目(批准号:60474022)
关键词 粗糙集 拓扑 内部算子 闭包算子 Rough set, Topology, Interior operator, Closure operator
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参考文献13

  • 1Pawlak Z. Rough sets. International Journal of Computer and Information Science, 1982,11: 341-356 被引量:1
  • 2Pawlak Z. Rough sets: Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Boston, 1991 被引量:1
  • 3Yao Y Y. Two views of the theory of rough sets in finite universes[J]. International Journal of Approximate Reasoning, 1996,15:291-317 被引量:1
  • 4Yao Y Y. Relational interpretations of neighborhood operators and rough set approximation operators [J]. Information Sciences, 1998,101 : 239-259 被引量:1
  • 5Kortelainen J. On the relationship between modified sets, topological spaces and rough sets [J]. Fuzzy Sets and Systems, 1994, 61: 91-95 被引量:1
  • 6Lashin E F, Kozae A M, Abo Khadra A A, et al. Rough set theory for topological spaces [J]. International Journal of Approximate Reasoning, 2005,40: 35-43 被引量:1
  • 7Kuncheva L I. Fuzzy rough sets: Application to feature selection [J]. Fuzzy Sets and Systems, 1992,51: 147-153 被引量:1
  • 8Dubois D, Prade H. Rough fuzzy sets and rough fuzzy sets [J]. International Journal of General Systems, 1990,17:191-209 被引量:1
  • 9Thiele H. Fuzzy rough sets versus rough fuzzy sets-An interpretation and a comparative study using concepts of modal logics [C]. In: Proc. of 5^th European Congress on Intelligent Technigues and Soft Computing, Aachen, Germany, 1997,9: 159-167 被引量:1
  • 10Morsi N N, Yakout M M. Axiomatics for fuzzy rough sets [J]. Fuzzy Sets and Systems, 1998,100 : 327-342 被引量:1

二级参考文献9

  • 1Pawlak Z.Rough sets[J].International Journal of Computer and Information Science,1982,11(5):341-356. 被引量:1
  • 2Pawlak Z.Rough Sets:Theoretical Aspects of Reasoning About Data[M].Boston:Kluwer Academic Publishers,1991. 被引量:1
  • 3Kuncheva L I.Fuzzy rough sets:Application to feature selection[J].Fuzzy Sets and Systems,1992,51(2):147-153. 被引量:1
  • 4Dubois D,Prade H.Rough fuzzy sets and fuzzy rough sets[J].International Journal of General Systems,1990,17(2):191-209. 被引量:1
  • 5Thiele H.Fuzzy rough sets versus rough fuzzy sets-An interpretation and a comparative study using concepts of modal logics[A].In:Proc of 5th European Congress on Intelligent Technigues and Soft Computing[C].Germany:Aachen,1997.159-167. 被引量:1
  • 6Morsi N N,Yakout M M.Axiomatics for fuzzy rough sets[J].Fuzzy Sets and Systems,1998,100:327-342. 被引量:1
  • 7Yao Y Y.Two views of the theory of rough sets in finite universes[J].International Journal of Approximate Reasoning,1996,15(3):291-317. 被引量:1
  • 8Kortelainen J.On relationship between modified sets,topological spaces and rough sets[J].Fuzzy Sets and Systems,1994,61(1):91-95. 被引量:1
  • 9Zadeh L A.Outline of a new approach to the analysis of complex systems and decision processes[J].IEEE Trans.Systems Man and Cybernet.,1973,(3):28-44. 被引量:1

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同被引文献125

引证文献12

二级引证文献16

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