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Using single axioms to characterize (S, T)-intuitionistic fuzzy rough approximation operators

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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 (S, T)-intuitionistic fuzzy rough approximation operators are then explored. Different sets of independent axioms for characterizing the essential properties of (S, T)-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.

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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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Authors and Affiliations

  1. School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan, 316022, Zhejiang, People’s Republic of China

    Wei-Zhi Wu & Xia Wang

  2. Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province, Zhejiang Ocean University, Zhoushan, 316022, Zhejiang, People’s Republic of China

    Wei-Zhi Wu & Xia Wang

  3. College of Computer and Communication Engineering, Chinese University of Petroleum, Qingdao, 266580, Shandong, People’s Republic of China

    Ming-Wen Shao

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  1. Wei-Zhi Wu
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  2. Ming-Wen Shao
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  3. Xia Wang
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Correspondence to Wei-Zhi Wu.

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Wu, WZ., Shao, MW. & Wang, X. Using single axioms to characterize (S, T)-intuitionistic fuzzy rough approximation operators. Int. J. Mach. Learn. & Cyber. 10, 27–42 (2019). https://doi.org/10.1007/s13042-017-0696-2

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  • DOI: https://doi.org/10.1007/s13042-017-0696-2

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