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Axiomatic Characterizations of Reflexive and \(\mathcal {T}\)-Transitive \(\mathcal {I}\)-Intuitionistic Fuzzy Rough Approximation Operators

  • Wei-Zhi Wu
  • You-Hong Xu
  • Tong-Jun Li
  • Xia Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9437)

Abstract

Axiomatic characterizations of approximation operators are important in the study of rough set theory. In this paper, axiomatic characterizations of relation-based intuitionistic fuzzy rough approximation operators determined by an intuitionistic fuzzy implication operator \(\mathcal{I}\) are investigated. We present a set of axioms of lower/upper \(\mathcal{I}\)-intuitionistic fuzzy set-theoretic operator which is necessary and sufficient for the existence of an intuitionistic fuzzy relation producing the same operator. We show that the lower and upper \(\mathcal{I}\)-intuitionistic fuzzy rough approximation operators generated by an arbitrary intuitionistic fuzzy relation can be described by single axioms. Moreover, the \(\mathcal{I}\)-intuitionistic fuzzy rough approximation operators generated by reflexive and \(\mathcal{T}\)-transitive intuitionistic fuzzy relations can also be characterized by single axioms.

Keywords

Approximation operators Intuitionistic fuzzy implicators Intuitionistic fuzzy rough sets Intuitionistic fuzzy sets Rough sets 

Notes

Acknowledgement

This work was supported by grants from the National Natural Science Foundation of China (Nos. 61272021, 61202206, and 61173181), and the Zhejiang Provincial Natural Science Foundation of China (Nos. LZ12F03002 and LY14F030001).

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© Springer International Publishing Switzerland 2015

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Authors and Affiliations

  • Wei-Zhi Wu
    • 1
    • 2
  • You-Hong Xu
    • 1
    • 2
  • Tong-Jun Li
    • 1
    • 2
  • Xia Wang
    • 1
    • 2
  1. 1.School of Mathematics, Physics and Information ScienceZhejiang Ocean UniversityZhoushanChina
  2. 2.Key Laboratory of Oceanographic Big Data Mining & Application of Zhejiang ProvinceZhejiang Ocean UniversityZhoushanChina

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