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An integrated cubic Pythagorean fuzzy MAIRCA model with novel variation coefficient similarity measure for food safety risk assessment
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  • Published: 27 February 2026

An integrated cubic Pythagorean fuzzy MAIRCA model with novel variation coefficient similarity measure for food safety risk assessment

  • Zhe Liu1,2,
  • Zeliang Weng3,
  • Amel Ksibi4,
  • Narinderjit Singh Sawaran Singh5,
  • Mohamed Abbas6,7,
  • Himanshu Dhumras8 &
  • …
  • Mehdi Hosseinzadeh9,10 

Scientific Reports , Article number:  (2026) Cite this article

We are providing an unedited version of this manuscript to give early access to its findings. Before final publication, the manuscript will undergo further editing. Please note there may be errors present which affect the content, and all legal disclaimers apply.

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  • Engineering
  • Mathematics and computing

Abstract

Food safety risk assessment is a complex multi-criteria decision-making (MCDM) issue characterized by high uncertainty in both data and expert opinions. Traditional MCDM methods struggle to effectively manage this uncertainty and subjectivity. This paper extends the multi-attributive ideal-real comparative analysis (MAIRCA) method to an uncertain decision-making environment by embedding it within a cubic Pythagorean fuzzy (CuPyF) framework, integrating a variation coefficient similarity measure (VCSM) and the rank-sum (RS) method. Cubic Pythagorean fuzzy sets (CuPyFSs) are used to represent both precise and interval-valued information, enabling better uncertainty modeling. The proposed VCSM objectively determines criteria weights, while the RS method provides subjective weights, leading to balanced comprehensive weighting. The extended CuPyF-based MAIRCA method is then applied to rank alternatives and select the optimal solution. A food safety case study validates the model, demonstrating that it delivers stable, discriminative, and interpretable results, outperforming traditional MCDM models and offering policymakers a reliable and scientific tool for food safety risk management.

Data availability

Data information is included in this paper.

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Funding

This study was funded by Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2026R759), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia. The authors extend their appreciation to University Higher Education Fund for funding this research work under Research Support Program for Central labs at King Khalid University through the project number CL/CO/A/6.

Author information

Authors and Affiliations

  1. College of Mathematics and Computer, Xinyu University, Xinyu, 338004, China

    Zhe Liu

  2. Research Fellow, Shinawatra University, Pathum Thani, 12160, Thailand

    Zhe Liu

  3. School of Computer Science and Technology, Hainan University, Haikou, 570228, China

    Zeliang Weng

  4. Department of Information Systems, College of Computer and Information Sciences, Princess Nourah bint Abdulrahman University, 11671, Riyadh, Saudi Arabia

    Amel Ksibi

  5. Faculty of Data Science and Information Technology, INTI International University, Nilai, 71800, Negeri Sembilan, Malaysia

    Narinderjit Singh Sawaran Singh

  6. Central Labs, King Khalid University, AlQura’a, Abha, P.O. Box 960, Saudi Arabia

    Mohamed Abbas

  7. Electrical Engineering Department, College of Engineering, King Khalid University, Abha, 61421, Saudi Arabia

    Mohamed Abbas

  8. School of Management, Shanghai University, Shanghai, 200444, China

    Himanshu Dhumras

  9. School of Engineering and Technology , Duy Tan University, Da Nang, Vietnam

    Mehdi Hosseinzadeh

  10. Department of AI, School of Computer Science and Engineering, Galgotias University, Greater Noida, India

    Mehdi Hosseinzadeh

Authors
  1. Zhe Liu
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  2. Zeliang Weng
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  3. Amel Ksibi
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  4. Narinderjit Singh Sawaran Singh
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  5. Mohamed Abbas
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  6. Himanshu Dhumras
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  7. Mehdi Hosseinzadeh
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Contributions

Z. Liu: Conceptualization, Methodology, Writing - original draft, Writing - review & editing. Z. Weng: Investigation, Validation, Writing - original draft. A. Ksibi: Formal analysis, Funding, Writing - review & editing, Supervision. N.S.S. Singh: Validation, Writing - review & editing. M. Abbas: Formal analysis, Funding, Writing - review & editing. H. Dhumras: Visualization, Writing - original draft. M. Hosseinzadeh: Investigation, Writing - review & editing.

Corresponding authors

Correspondence to Zhe Liu or Amel Ksibi.

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The authors declare no competing interests.

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Liu, Z., Weng, Z., Ksibi, A. et al. An integrated cubic Pythagorean fuzzy MAIRCA model with novel variation coefficient similarity measure for food safety risk assessment. Sci Rep (2026). https://doi.org/10.1038/s41598-026-39302-z

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  • Received: 30 November 2025

  • Accepted: 04 February 2026

  • Published: 27 February 2026

  • DOI: https://doi.org/10.1038/s41598-026-39302-z

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Keywords

  • Cubic Pythagorean fuzzy sets
  • Decision-making
  • Variation coefficient similarity measure
  • Food safety
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