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Using single axioms to characterize (ST)-intuitionistic fuzzy rough approximation operators

  • Wei-Zhi WuEmail author
  • Ming-Wen Shao
  • Xia Wang
Original Article

Abstract

In this paper axiomatic characterizations of relation-based intuitionistic fuzzy rough approximation operators determined by an intuitionistic fuzzy triangular norm T and its dual intuitionistic fuzzy triangular conorm S on \([0, 1]\times [0, 1]\) are proposed. The constructive definitions and properties of S-lower and T-upper intuitionistic fuzzy rough approximation operators are first introduced. Operator-oriented characterizations of (ST)-intuitionistic fuzzy rough approximation operators are then explored. Different sets of independent axioms for characterizing the essential properties of (ST)-intuitionistic fuzzy rough approximation operators generated by various intuitionistic fuzzy relations are presented. Finally, it is examined that these sets of axioms can all be replaced by single axioms.

Keywords

Approximation operators Intuitionistic fuzzy rough sets Intuitionistic fuzzy sets Rough sets Triangular norms 

Notes

Acknowledgements

The authors would like to thank the anonymous referees and the Editor for their valuable comments and suggestions. This work was supported by grants from the National Natural Science Foundation of China (Nos. 41631179, 61573321, 61272021, 61673396, and 61363056) and the Open Foundation from Marine Sciences in the Most Important Subjects of Zhejiang (No. 20160102).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.School of Mathematics, Physics and Information ScienceZhejiang Ocean UniversityZhoushanPeople’s Republic of China
  2. 2.Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang ProvinceZhejiang Ocean UniversityZhoushanPeople’s Republic of China
  3. 3.College of Computer and Communication EngineeringChinese University of PetroleumQingdaoPeople’s Republic of China

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