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基于直觉模糊合成关系的直觉模糊粗糙集
  • ISSN号：1005-3085
  • 期刊名称：《工程数学学报》
  • 时间：0
  • 分类：O159[理学—数学;理学—基础数学]
  • 作者机构：[1]江苏省扬中市高级中学,镇江212200, [2]漳州师范学院数学与信息科学系,福建漳州363000
  • 相关基金：国家自然科学基金（10971185;10971186;11061004）.
作者： 汤小江[1,2], 李克典[2]
关键词： 直觉模糊集, 直觉模糊合成关系, 直觉模糊粗糙集, 直觉模糊拓扑, intuitionistic fuzzy sets, the composition of intuitionistic fuzzy relations, intuitionistic fuzzy rough sets, intuitionistic fuzzy topological spaces
中文摘要：

利用直觉模糊合成关系定义直觉模糊粗糙集，讨论了直觉模糊关系分别为自反、对称、传递时所对应的上、下近似算子的性质．在有限论域U中，研究了自反直觉模糊关系所诱导的直觉模糊拓扑空间中直觉模糊闭包、内部算子与相对应的上、下近似算子的关系．

英文摘要：

Just like rough set theory, intuitionistic fuzzy （IF） set theory addresses the topic of dealing with imperfect knowledge. Recent studies have shown how both theories can be combined into a more flexible, expressive framework for modelling and processing incomplete information in information systems. In this paper, the model of IF rough sets based on the composition of IF relations is introduced. Basic properties of the IF rough approximation operators are then discussed in the cases of reflexive, symmetric and transitive relations. Furthermore, we see that in the finite space an reflexive relation can also generate IF topological spaces and show that the lower and upper IF rough approximation operators are, respectively, the interior and closure operators of the IF topological spaces.

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期刊信息
  • 《工程数学学报》
  • 北大核心期刊（2011版）
  • 主管单位:教育部
  • 主办单位:西安交通大学
  • 主编：李大潜
  • 地址：西宁市咸宁西路28号西安交通大学数学与统计学院
  • 邮编：710049
  • 邮箱：jgsx@mail.xjtu.edu.cn
  • 电话：029-82667877
  • 国际标准刊号：ISSN：1005-3085
  • 国内统一刊号：ISSN：61-1269/O1
  • 邮发代号:
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  • 被引量:6741