A novel multi-granularity variable precision neutrosophic rough set and group decision-making application with three strategies

Hongyuan Zheng; Chunxin Bo; Lingqiang Li; Lu Wang; Wenjie Jiang; Hongyuan Zheng; Chunxin Bo; Lingqiang Li; Lu Wang; Wenjie Jiang

doi:10.3934/math.20251029

AIMS Mathematics

2025, Volume 10, Issue 10: 23187-23219. doi: 10.3934/math.20251029

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A novel multi-granularity variable precision neutrosophic rough set and group decision-making application with three strategies

School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, China

Received: 09 July 2025 Revised: 14 September 2025 Accepted: 28 September 2025 Published: 13 October 2025
MSC : 03E72, 90B50, 94D05

This paper proposes a novel neutrosophic rough set model to solve group decision-making problems. First, we proposed a novel multi-granularity variable-precision neutrosophic rough set model, which included three basic models: optimistic, pessimistic, and compromise. Second, the properties of the upper and lower approximations of the multi-granularity variable-precision neutrosophic rough set were investigated by means of the residual implications of triangular norms, and their favorable algebraic properties were proved. Finally, the effectiveness, stability, and sensitivity of the three proposed models were verified through a multi-attribute group decision-making example in a single universe, and the experimental results showed that this method could accurately rank the targets. In summary, our method provided multiple strategies and fault tolerance.
- neutrosophic rough set,
- multi-granularity,
- variable precision,
- group decision-making
Citation: Hongyuan Zheng, Chunxin Bo, Lingqiang Li, Lu Wang, Wenjie Jiang. A novel multi-granularity variable precision neutrosophic rough set and group decision-making application with three strategies[J]. AIMS Mathematics, 2025, 10(10): 23187-23219. doi: 10.3934/math.20251029

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Abstract

This paper proposes a novel neutrosophic rough set model to solve group decision-making problems. First, we proposed a novel multi-granularity variable-precision neutrosophic rough set model, which included three basic models: optimistic, pessimistic, and compromise. Second, the properties of the upper and lower approximations of the multi-granularity variable-precision neutrosophic rough set were investigated by means of the residual implications of triangular norms, and their favorable algebraic properties were proved. Finally, the effectiveness, stability, and sensitivity of the three proposed models were verified through a multi-attribute group decision-making example in a single universe, and the experimental results showed that this method could accurately rank the targets. In summary, our method provided multiple strategies and fault tolerance.

References

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