On the Intuitionistic Fuzzy Topological Structures of Rough Intuitionistic Fuzzy Sets

  • You-Hong Xu
  • Wei-Zhi WuEmail author
  • Guoyin Wang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8449)


A rough intuitionistic fuzzy set is the result of approximation of an intuitionistic fuzzy set with respect to a crisp approximation space. In this paper, we investigate topological structures of rough intuitionistic fuzzy sets. We first show that a reflexive crisp rough approximation space can induce an intuitionistic fuzzy Alexandrov space. It is proved that the lower and upper rough intuitionistic fuzzy approximation operators are, respectively, an intuitionistic fuzzy interior operator and an intuitionistic fuzzy closure operator if and only if the binary relation in the crisp approximation space is reflexive and transitive. We then verify that a similarity crisp approximation space can produce an intuitionistic fuzzy clopen topological space. We further examine sufficient and necessary conditions that an intuitionistic fuzzy interior (closure, respectively) operator derived from an intuitionistic fuzzy topological space can associate with a reflexive and transitive crisp relation such that the induced lower (upper, respectively) rough intuitionistic fuzzy approximation operator is exactly the intuitionistic fuzzy interior (closure, respectively) operator.


Approximation operators Binary relations Intuitionistic fuzzy sets Intuitionistic fuzzy topologies Rough intuitionistic fuzzy sets Rough sets 



This work was supported by grants from the National Natural Science Foundation of China (Nos. 61272021, 61075120, 11071284, 61202206, and 61173181), the Zhejiang Provincial Natural Science Foundation of China (No. LZ12F03002), and Chongqing Key Laboratory of Computational Intelligence (No. CQ-LCI-2013-01).


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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.School of Mathematics, Physics and Information ScienceZhejiang Ocean UniversityZhoushanPeople’s Republic of China
  2. 2.Chongqing Key Laboratory of Computational IntelligenceChongqing University of Posts and TelecommunicationsChongqingPeople’s Republic of China

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