SavedAdd your journal

Journals / ALKÜ Fen Bilimleri Dergisi / 2026 / Sayı: 2

A Trapezoidal Pythagorean Fuzzy AHP–PROMETHEE Framework for Multi-Criteria Group Decision Making with an Illustrative Supplier Selection Example

Çok Kriterli Grup Karar Verme için Trapezoidal Pisagor Bulanık AHP–PROMETHEE Bütünleşik Yaklaşımı: Tedarikçi Seçimi Örneği

Didem Sarı Ay(ALANYA ALAADDIN KEYKUBAT UNIVERSITY)0000-0002-9403-9015
Pages
—
Publication Date
2026-07-08
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The effectiveness of the proposed method is demonstrated through comparative analysis using data reported in an existing study and through a supplier selection illustration based on hypothetical data.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Multi-criteria decision-making problems often involve uncertain, imprecise, and subjective information, requiring advanced fuzzy modeling approaches.
📊
Key Findings & Data:A pairwise comparison approach based on the Hamming distance is adopted and integrated into the ranking procedure.
💡
Conclusion & Impact:The effectiveness of the proposed method is demonstrated through comparative analysis using data reported in an existing study and through a supplier selection illustration based on hypothetical data.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Çok kriterli karar verme · PROMETHEE · trapezoidal Pythagorean bulanık kümeler

Abstract

Multi-criteria decision-making problems often involve uncertain, imprecise, and subjective information, requiring advanced fuzzy modeling approaches. Among widely used decision-making techniques, the Preference Ranking Organization Method for Enrichment of Evaluations is valued for its intuitive outranking structure and strong discriminative capability. This study proposes an extension of this method under a trapezoidal Pythagorean fuzzy environment. In the proposed framework, decision makers’ evaluations are represented using trapezoidal Pythagorean fuzzy numbers. A pairwise comparison approach based on the Hamming distance is adopted and integrated into the ranking procedure. In addition, the Analytic Hierarchy Process is used to determine criteria weights, resulting in an integrated group decision-making framework. The effectiveness of the proposed method is demonstrated through comparative analysis using data reported in an existing study and through a supplier selection illustration based on hypothetical data.

Özet

Çok kriterli karar verme problemleri kesin olmayan ve öznel bilgiler içermekte olup, bu durum gelişmiş bulanık modelleme yaklaşımlarının kullanılmasını gerekli kılmaktadır. Yaygın olarak kullanılan çok kriterli karar verme yöntemleri arasında PROMETHEE yöntemi, sezgisel üstünlük yapısı ve güçlü ayırt edicilik özelliği nedeniyle öne çıkmaktadır. Bu çalışmada, PROMETHEE yöntemi trapezoidal Pythagorean bulanık yapı altında genişletilmiştir. Önerilen çerçevede, karar vericilerin değerlendirmeleri trapezoidal Pythagorean bulanik sayılar kullanılarak temsil edilmektedir. Trapezoidal Pythagorean bulanik değerlendirmelerin karşılaştırılmasında Hamming uzaklığına dayalı ikili karşılaştırma yaklaşımı sıralama sürecine entegre edilmiştir. Ayrıca, kriter ağırlıklarının belirlenmesinde Analitik Hiyerarşi Süreci kullanılarak grup değerlendirme problemleri için bütünleşik bir karar verme sureci oluşturulmuştur. Literatürde veri seti sunulan mevcut bir çalışma ile karşılaştırmalı analiz yapılarak karar verme modelinin uygulanabilirliği gösterilmiştir. Ayrıca, varsayımsal veriler kullanılarak modelin uygulanabilirliği bir tedarikçi seçimi örnek uygulaması üzerinden gösterilmiştir.

🔖

Cite This Article

Ay, D. S. (2026). A Trapezoidal Pythagorean Fuzzy AHP–PROMETHEE Framework for Multi-Criteria Group Decision Making with an Illustrative Supplier Selection Example. ALKÜ Fen Bilimleri Dergisi, Sayı: 2. https://doi.org/10.46740/alku.1871228

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (57)

  1. Chai, N.J., W.L. Zhou, and Z.G. Jiang, Sustainable supplier selection using an intuitionistic and interval-valued fuzzy MCDM approach based on cumulative prospect theory. Information Sciences, 2023. 626: p. 710–737.
  2. Ho, W., X.W. Xu, and P.K. Dey, Multi-criteria decision-making approaches for supplier evaluation and selection: A literature review. European Journal of Operational Research, 2010. 202(1): p. 16–24.
  3. Rasmussen, A., et al., Supplier selection for aerospace & defense industry through MCDM methods. Cleaner Engineering and Technology, 2023. 12.
  4. Singh, R.R., D. Zindani, and S.R. Maity, A novel fuzzy-prospect theory approach for hydrogen fuel cell component supplier selection for automotive industry. Expert Systems with Applications, 2024. 246.
  5. Beheshtinia, M.A. and S. Omidi, A hybrid MCDM approach for performance evaluation in the banking industry. Kybernetes, 2017. 46(8): p. 1386–1407.
  6. Shayganmehr, M. and G.A. Montazer, A novel hybrid assessment model to evaluate e-services websites of Iranian municipalities. Artificial Intelligence Review, 2021. 54(8): p. 5699–5733.
  7. Fallahpour, A., et al., A decision support model for sustainable supplier selection in sustainable supply chain management. Computers & Industrial Engineering, 2017. 105: p. 391–410.
  8. Govindan, K., R. Khodaverdi, and A. Jafarian, A fuzzy multi criteria approach for measuring sustainability performance of a supplier based on triple bottom line approach. Journal of Cleaner Production, 2013. 47: p. 345–354.
  9. Govindan, K., R. Khodaverdi, and A. Vafadarnikjoo, Intuitionistic fuzzy based DEMATEL method for developing green practices and performances in a green supply chain. Expert Systems with Applications, 2015. 42(20): p. 7207–7220.
  10. Molla, M.U., B.C. Giri, and P. Biswas, Extended PROMETHEE method with Pythagorean fuzzy sets for medical diagnosis problems. Soft Computing, 2021. 25(6): p. 4503–4512.
  11. Mohammed, A., I. Harris, and K. Govindan, A hybrid MCDM-FMOO approach for sustainable supplier selection and order allocation. International Journal of Production Economics, 2019. 217: p. 171–184.
  12. Stevic, Z., et al., Sustainable supplier selection in healthcare industries using a new MCDM method: Measurement of alternatives and ranking according to COmpromise solution (MARCOS). Computers & Industrial Engineering, 2020. 140.
  13. Venkatesh, V., et al., Supplier selection in blood bags manufacturing industry using TOPSIS model. International Journal of Operational Research, 2015. 24(4): p. 461–488.
  14. Le, M.T., Strategic Prioritization for Sustainable Development in the Logistics Industry: A FAHP-NFAD Approach. Applied Sciences-Basel, 2025. 15(8).
  15. Atanassov, K.T., Intuitionistic Fuzzy-Sets. Fuzzy Sets and Systems, 1986. 20(1): p. 87–96.
  16. Zadeh, L.A., Fuzzy Sets. Information and Control, 1965. 8(3): p. 338–&.
  17. Marinato, V.H.A., et al., Assessing the Quality of Virtual Student Internships in Brazilian Organizations: Potential and Use of Fuzzy TOPSIS Class. Appliedmath, 2025. 5(3).
  18. Trifunovic, M., et al., Fuzzy MCDM Methodology for Analysis of Fibre Laser Cutting Process. Applied Sciences-Basel, 2025. 15(13).
  19. Ma, Z.M. and Z.S. Xu, Symmetric Pythagorean Fuzzy Weighted Geometric/Averaging Operators and Their Application in Multicriteria Decision-Making Problems. International Journal of Intelligent Systems, 2016. 31(12): p. 1198–1219.
  20. Pérez-Domínguez, L., et al., MOORA under Pythagorean Fuzzy Set for Multiple Criteria Decision Making. Complexity, 2018.
  21. Yager, R.R., Pythagorean Membership Grades in Multicriteria Decision Making. Ieee Transactions on Fuzzy Systems, 2014. 22(4): p. 958–965.
  22. Zhang, X.L. and Z.S. Xu, Extension of TOPSIS to Multiple Criteria Decision Making with Pythagorean Fuzzy Sets. International Journal of Intelligent Systems, 2014. 29(12): p. 1061–1078.
  23. Shakeel, M. and S. Abdullah, Some induced interval-valued Pythagorean trapezoidal fuzzy averaging aggregation operators based on Einstein operations and their application in group decision-making. Computational and Applied Mathematics, 2019. 38(3): p. 97.
  24. Shakeel, M., et al., Pythagorean trapezoidal fuzzy geometric aggregation operators based on Einstein operations and their application in group decision making. Journal of Intelligent & Fuzzy Systems, 2019. 36(1): p. 309–324.
  25. Shakeel, M., et al., Averaging aggregation operators with pythagorean trapezoidal fuzzy numbers and their application to group decision making. Journal of Intelligent & Fuzzy Systems, 2019. 36(2): p. 1899–1915.
  26. Xian, S.D., et al., A new trapezoidal Pythagorean fuzzy linguistic entropic combined ordered weighted averaging operator and its application for enterprise location. International Journal of Intelligent Systems, 2018. 33(9): p. 1880–1899.
  27. Ren, H.P. and L.J. Luo, A novel distance of intuitionistic trapezoidal fuzzy numbers and its-based prospect theory algorithm in multi-attribute decision making model. Mathematical Biosciences and Engineering, 2020. 17(4): p. 2905–2922.
  28. Shakeel, M., et al., Ranking methodology of induced Pythagorean trapezoidal fuzzy aggregation operators based on Einstein operations in group decision making. Soft Computing, 2020. 24(10): p. 7319–7334.
  29. Hamming, R.W., Error Detecting and Error Correcting Codes. Bell System Technical Journal, 1950. 29(2): p. 147–160.
  30. Hamming, R.W., Error Detecting and Error Correcting Codes (1950). Ideas That Created the Future, 2021: p. 135–146.
  31. Alkouri, A.M. and A.R. Salleh, Linguistic variable, hedges and several distances on complex fuzzy sets. Journal of Intelligent & Fuzzy Systems, 2014. 26(5): p. 2527–2535.
  32. Dai, S.S., L.Q. Bi, and B. Hu, Distance Measures between the Interval-Valued Complex Fuzzy Sets. Mathematics, 2019. 7(6).
  33. Izadikhah, M., Using the Hamming distance to extend TOPSIS in a fuzzy environment. Journal of Computational and Applied Mathematics, 2009. 231(1): p. 200–207.
  34. Song, H.F., et al., New Distance Measures between the Interval-Valued Complex Fuzzy Sets with Applications to Decision-Making. Mathematical Problems in Engineering, 2021. 2021.
  35. Zeng, S.Z., W.H. Su, and J. Chen, Fuzzy decision making with induced heavy aggregation operators and distance measures. Journal of Intelligent & Fuzzy Systems, 2014. 26(1): p. 127–135.
  36. Saaty, T.L., Scaling Method for Priorities in Hierarchical Structures. Journal of Mathematical Psychology, 1977. 15(3): p. 234–281.
  37. Saaty, T.L., The analytic hierarchy process: planning, priority setting, resource allocation. 1980, New York; London: McGraw-Hill International Book Co. xiii, 287 p.
  38. Saaty, T.L., Decision making with the analytic hierarchy process. International journal of services sciences, 2008. 1(1): p. 83–98.
  39. Yager, R.R., Pythagorean Fuzzy Subsets. Proceedings of the 2013 Joint Ifsa World Congress and Nafips Annual Meeting (Ifsa/Nafips), 2013: p. 57–61.
  40. Kuncova, M. and J. Seknickova, Two-stage weighted PROMETHEE II with results' visualization. Central European Journal of Operations Research, 2022. 30(2): p. 547–571.
  41. Wang, J.J. and D.L. Yang, Using a hybrid multi-criteria decision aid method for information systems outsourcing. Computers & Operations Research, 2007. 34(12): p. 3691–3700.
  42. Brans, J.P., P. Vincke, and B. Mareschal, How to Select and How to Rank Projects - the Promethee Method. European Journal of Operational Research, 1986. 24(2): p. 228–238.
  43. Giri, B.C., M.U. Molla, and P. Biswas, Pythagorean fuzzy DEMATEL method for supplier selection in sustainable supply chain management. Expert Systems with Applications, 2022. 193.
  44. Khan, M.S.A., et al., Pythagorean fuzzy prioritized aggregation operators and their application to multi-attribute group decision making. Granular Computing, 2019. 4(2): p. 249–263.
  45. Momena, A.F. and N. Abu-Zahra, A novel aggregation method for generating Pythagorean fuzzy numbers in multiple criteria group decision making: An application to materials selection. Cogent Engineering, 2021. 8(1).
  46. Liu, P.D. and X.C. Yu, Density Aggregation Operators Based on the Intuitionistic Trapezoidal Fuzzy Numbers for Multiple Attribute Decision Making. Technological and Economic Development of Economy, 2013. 19: p. S454–S470.
  47. Zhou, W. and J.M. He, Interval-valued intuitionistic fuzzy ordered precise weighted aggregation operator and its application in group decision making. Technological and Economic Development of Economy, 2014. 20(4): p. 648–672.
  48. Wan, S.P. and J.Y. Dong, Multi-Attribute Group Decision Making with Trapezoidal Intuitionistic Fuzzy Numbers and Application to Stock Selection. Informatica, 2014. 25(4): p. 663–697.
  49. Wang, J.Q. and Z. Zhang, Aggregation operators on intuitionistic trapezoidal fuzzy number and its application to multi-criteria decision making problems. Journal of Systems Engineering and Electronics, 2009. 20(2): p. 321–326.
  50. Xu, Z.S. and R.R. Yager, Some geometric aggregation operators based on intuitionistic fuzzy sets. International Journal of General Systems, 2006. 35(4): p. 417–433.
  51. Debnath, B., et al., An integrated stepwise weight assessment ratio analysis and weighted aggregated sum product assessment framework for sustainable supplier selection in the healthcare supply chains. Supply Chain Analytics, 2023. 1.
  52. Nie, S., et al., Green Supplier Selection With a Continuous Interval-Valued Linguistic TODIM Method. Ieee Access, 2019. 7: p. 124315–124328.
  53. Ulutas, A., et al., Developing of a Novel Integrated MCDM MULTIMOOSRAL Approach for Supplier Selection. Informatica, 2021. 32(1): p. 145–161.
  54. Liu, H.C., et al., A new integrated MCDM model for sustainable supplier selection under interval-valued intuitionistic uncertain linguistic environment. Information Sciences, 2019. 486: p. 254–270.
  55. Alipour, M., et al., A new Pythagorean fuzzy-based decision-making method through entropy measure for fuel cell and hydrogen components supplier selection. Energy, 2021. 234.
  56. Abdullah, L., W. Chan, and A. Afshari, Application of PROMETHEE method for green supplier selection: a comparative result based on preference functions. Journal of Industrial Engineering International, 2019. 15(2): p. 271–285.
  57. Saaty, T.L., The analytic hierarchy process: planning, priority setting, resource allocation. 1980, New York; London: McGraw-Hill International Book Co. xiii, 287 p.