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Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing pp 218–229Cite as

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

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Part of the book series: Lecture Notes in Computer Science ((LNAI,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.

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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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Authors and Affiliations

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

    Wei-Zhi Wu, You-Hong Xu, Tong-Jun Li & Xia Wang

  2. Key Laboratory of Oceanographic Big Data Mining & Application of Zhejiang Province, Zhejiang Ocean University, Zhoushan, 316022, Zhejiang, China

    Wei-Zhi Wu, You-Hong Xu, Tong-Jun Li & Xia Wang

Authors
  1. Wei-Zhi Wu
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  2. You-Hong Xu
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  3. Tong-Jun Li
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  4. Xia Wang
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Corresponding author

Correspondence to Wei-Zhi Wu .

Editor information

Editors and Affiliations

  1. University of Regina, Regina, SK, Canada

    Yiyu Yao

  2. Tianjin University, Tianjin, China

    Qinghua Hu

  3. Chongqing University of Posts and Telecommunications, Chongqing, China

    Hong Yu

  4. University of Kansas, Lawrence, KS, USA

    Jerzy W. Grzymala-Busse

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Wu, WZ., Xu, YH., Li, TJ., Wang, X. (2015). Axiomatic Characterizations of Reflexive and \(\mathcal {T}\)-Transitive \(\mathcal {I}\)-Intuitionistic Fuzzy Rough Approximation Operators. In: Yao, Y., Hu, Q., Yu, H., Grzymala-Busse, J.W. (eds) Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. Lecture Notes in Computer Science(), vol 9437. Springer, Cham. https://doi.org/10.1007/978-3-319-25783-9_20

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  • DOI: https://doi.org/10.1007/978-3-319-25783-9_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25782-2

  • Online ISBN: 978-3-319-25783-9

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