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Several L-fuzzy variable precision rough sets and their axiomatic characterizations

  • Foundation, algebraic, and analytical methods in soft computing
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Abstract

Axiomatization is a significant and challenging task in the field of fuzzy variable precision rough sets, where research is currently limited. This paper aims to address this gap by defining and characterizing 14 types of L-fuzzy variable precision rough sets (LFVPRS for short). First, we introduce three fundamental LFVPRSs generated by Euclidean, mediate, and associate L-fuzzy relations. Second, we present their single axiomatic characterizations using the product of L-fuzzy sets. Lastly, we provide single axiomatic characterizations for another 11 types of LFVPRSs, which are generated by various compositions of reflexive, transitive, symmetry, Euclidean, mediate, and associate L-fuzzy relations. These single axiomatic characterizations are entirely innovative and have not been explored, even in the context of classical rough sets and fuzzy rough sets.

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Acknowledgements

The authors thank the editor and the reviewers for their valuable comments and suggestions.

Funding

This work was supported by National Natural Science Foundation of China (No. 12171220), and Natural Science Foundation of Shandong Province (No. ZR2023MA079), and Discipline with Strong Characteristics of Liaocheng University—Intelligent Science and Technology under Grant 319462208.

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  1. College of Mathematics and Sciences, Liaocheng University, Liaocheng, China

    Qiu Jin & Ling-Qiang Li

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  1. Qiu Jin
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  2. Ling-Qiang Li
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All authors contributed equally and significantly in writing this paper.

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Correspondence to Ling-Qiang Li.

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Jin, Q., Li, LQ. Several L-fuzzy variable precision rough sets and their axiomatic characterizations. Soft Comput 27, 16429–16448 (2023). https://doi.org/10.1007/s00500-023-09183-9

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