Neutrosophic Z-number analytic hierarchy process: A framework for enhanced group decision-making under uncertainty

Authors

  • Phi-Hung Nguyen * Research Center of Applied Sciences, Faculty of Business, FPT University, Hanoi, 100000, Vietnam. https://orcid.org/0000-0003-3372-8287
  • Lan-Anh Thi Nguyen Research Center of Applied Sciences, Faculty of Business, FPT University, Hanoi, 100000, Vietnam.
  • Tra-Giang Vu Research Center of Applied Sciences, Faculty of Business, FPT University, Hanoi, 100000, Vietnam.
  • Minh-Thang Phan Research Center of Applied Sciences, Faculty of Business, FPT University, Hanoi, 100000, Vietnam.
  • Van-Hien Ngo Research Center of Applied Sciences, Faculty of Business, FPT University, Hanoi, 100000, Vietnam.
  • Dieu-Linh Do Research Center of Applied Sciences, Faculty of Business, FPT University, Hanoi, 100000, Vietnam.

https://doi.org/10.48313/uda.v2i1.68

Abstract

Multi-Criteria Decision-Making (MCDM) often faces challenges in handling uncertainty, imprecision, and unreliable expert judgments, limiting the effectiveness of traditional methods like the Analytic Hierarchy Process (AHP). This study proposes the Neutrosophic Z-Number AHP (NZN-AHP) method to enhance decision-making by addressing these complexities. The NZN-AHP method integrates Neutrosophic Z-Numbers (NZNs), which model truth, indeterminacy, falsity, and reliability, with AHP’s structured pairwise comparison framework. Linguistic scales and advanced aggregation operators, such as Dombi and Aczel–Alsina, are employed to process expert evaluations, ensuring robust handling of uncertain data. The NZN-AHP method achieves consistent outcomes (CR < 0.1), outperforming traditional and fuzzy AHP by incorporating reliability and indeterminacy, thus providing more accurate prioritization of criteria in complex decision-making scenarios. NZN-AHP offers a versatile and precise framework for MCDM, effectively capturing multifaceted uncertainties and enhancing decision-making across domains like logistics, finance, and strategic planning. It sets a foundation for future research into integrating NZNs with other MCDM methods, advancing the field of decision sciences.

Keywords:

Neutrosophic Z-number sets, AHP method, Neutrosophic sets, Z-numbers, Expert consensus, Uncertainty

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2025-03-22

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Vol. 2 No. 1 (2025): Uncertainty Discourse and Applications

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Articles

How to Cite

Nguyen, P.-H. ., Thi Nguyen, L.-A. ., Vu, T.-G., Phan, M.-T., Ngo, V.-H. ., & Do, D.-L. . (2025). Neutrosophic Z-number analytic hierarchy process: A framework for enhanced group decision-making under uncertainty. Uncertainty Discourse and Applications, 2(1), 76-98. https://doi.org/10.48313/uda.v2i1.68

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