An Enhanced Hierarchical Fuzzy TOPSIS-ANP Method for Supplier Selection in an Uncertain Environment

Khodadad Ouraki, Abdollah Hadi-Vencheh (), Ali Jamshidi and Amir Karbassi Yazdi
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Khodadad Ouraki: Department of Mathematics, Isf. C., Islamic Azad University, Isfahan 39998-8155, Iran
Abdollah Hadi-Vencheh: Department of Mathematics, Isf. C., Islamic Azad University, Isfahan 39998-8155, Iran
Ali Jamshidi: Department of Mathematics, Isf. C., Islamic Azad University, Isfahan 39998-8155, Iran
Amir Karbassi Yazdi: Departamento de Ingenieria, Industrial y de Sistemas, Facultad de Ingenieria, Universidad de Tarapaca, Arica 1010069, Chile

Mathematics, 2025, vol. 13, issue 21, 1-21

Abstract: This paper proposes an enhanced hierarchical fuzzy Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) integrated with the Analytic Network Process (ANP) for solving multi-criteria decision-making (MCDM) problems under uncertainty. Conventional fuzzy TOPSIS models often face significant challenges, such as restrictions to specific fuzzy number formats, difficulties in normalization when zero or very small values appear, and limited capacity to capture hierarchical interdependencies among criteria. To address these limitations, we develop a generalized fuzzy geometric mean approach for deriving weights from pairwise comparisons that can accommodate multiple fuzzy number types. Moreover, a novel normalization function is introduced, which ensures mathematically valid outcomes within the [0, 1] interval while avoiding division-by-zero and inconsistency issues. The proposed method is validated through both a numerical building selection problem and a practical supplier selection case study. Comparative analyses against established fuzzy MCDM models demonstrate the improved robustness, flexibility, and accuracy of the approach. Additionally, a sensitivity analysis confirms the stability of results with respect to variations in criteria weights, fuzzy number formats, and normalization techniques. These findings highlight the potential of the proposed fuzzy hierarchical TOPSIS-ANP framework as a reliable and practical decision support tool for complex real-world applications, including supply chain management and resource allocation under uncertainty.

Keywords: fuzzy MCDM; hierarchical TOPSIS; ANP; supplier selection; sensitivity analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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