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The variable precision fuzzy rough set based on overlap and grouping functions with double weight method to MADM

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Abstract

Variable precision fuzzy rough set (VPFRS) is widely utilized for handling various forms of uncertain information due to its fault-tolerant capability. However, a significant number of these rough sets fail to satisfy the inclusion property (lower approximation included in the upper approximation), posing potential risks in applications. Moreover, a common method of constructing the VPFRS is through triangular norms and triangular conorms. But in certain practical applications, the associative law of triangular norms and triangular conorms may not be essential. Overlap functions and grouping functions can effectively avoid this issue. Therefore, to address the limitations of existing models, we introduce the concept of VPFRS based on overlap and grouping functions, and apply it to a real multi-attribute decision-making problem. Firstly, we propose a novel VPFRS leveraging overlap and grouping functions, and demonstrate that it satisfies the generalized inclusion property. This solves the deficiency in VPFRSs not meeting the inclusion property to some extent. Additionally, with the help of the generalized inclusion property, we introduce a new objective method for computing attribute weights. Subsequently, by integrating the merits of the proposed VPFRS model and the PROMETHEE method, we develop a multi-attribute decision-making method with double weight. Finally, the validity of our decision-making method and weight calculation approach is substantiated through comparison and experimental analysis.

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Acknowledgements

The authors would like to thank the editors and the anonymous reviewers for their insightful and constructive comments and suggestions that have led to this improved version of the paper. This work was supported by National Natural Science Foundation of China (No. 12171220), 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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Authors and Affiliations

  1. Department of Mathematics, Liaocheng University, Liaocheng, 252059, P.R. China

    Zhengqi Shi, Lingqiang Li & Shurui Xie

  2. School of Science, Jimei University, Xiamen, 361021, P.R. China

    Jialiang Xie

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Contributions

Zhengqi Shi: Conceptualization, Investigation, Methodology, Resources, Software, Writing - original draft, Writing - review & editing. Lingqiang Li: Conceptualization, Methodology, Writing - original draft. Shurui Xie: Investigation, Resources. Jialiang Xie: Investigation, Resources.

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Correspondence to Lingqiang Li.

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Shi, Z., Li, L., Xie, S. et al. The variable precision fuzzy rough set based on overlap and grouping functions with double weight method to MADM. Appl Intell 54, 7696–7715 (2024). https://doi.org/10.1007/s10489-024-05554-3

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