Priorities for School Infrastructure Investment in the Face of Uncertainty: An Intuitionistic Fuzzy Multi-Criteria Decision-Making Method Employing the Frank Weighted Averaging Operator

Authors

DOI:

https://doi.org/10.66972/iscis21202624

Keywords:

Intuitionistic Fuzzy Number, Frank weighted average operator, TOPSIS, MOORA, VIKOR, WASPAS, CRITIC

Abstract

There is a need for a framework of decisions that is able to deal with the uncertainty and subjective nature of expert judgment as well as limited public funds. This paper presents an integrated multi-criteria decision-making approach using Intuitionistic Fuzzy Numbers and the Frank Weighted Averaging operator to prioritize school classroom building projects under a fixed capital budget. Four criteria—safety urgency, number of students affected, cost, and education impact—are measured by an IFN to reflect the membership, non-membership, and hesitancy built into expert assessments, and four candidate schools are assessed against these four criteria. The aggregation of the criteria into one fuzzy score for each alternative is done using a fuzzy operator, IFN-FWA, which is then converted to a crisp matrix using a score function. The obtained matrix is then assessed with five different MCDM methods (TOPSIS, WASPAS, VIKOR, MOORA, and CRITIC) to check the robustness of the ranking. The objective criterion weights are not subjectively assigned but are calculated with the CRITIC method, which will decrease subjectivity in the final recommendation. Although the mathematics involved in each method is different, the results consistently show that the top-ranked school is School4, followed by School2, School1, and School3, with a high level of agreement. The results validate that using the intuitionistic fuzzy aggregation proposed by Frank with multiple validated MCDM approaches can ensure the transparency, defensibility, and stability of the public infrastructure investment decision-making process under uncertainty.

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References

Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87–96. https://doi.org/10.1016/S0165-0114(86)80034-3

Xu, Z., & Yager, R. R. (2006). Some geometric aggregation operators based on intuitionistic fuzzy sets. International Journal of General Systems, 35(4), 417–433. https://doi.org/10.1080/03081070600574353

Dubois, D., & Prade, H. (1978). Operations on fuzzy numbers. International Journal of Systems Science, 9(6), 613–626. https://doi.org/10.1080/00207727808941724

Chang, S. S. L., & Zadeh, L. A. (1972). On fuzzy mapping and control. IEEE Transactions on Systems, Man, and Cybernetics, 2(1), 30–34. https://doi.org/10.1109/TSMC.1972.5408553

Burillo, P., Bustince, H., & Mohedano, V. (1994). Some definitions of intuitionistic fuzzy number: First properties. In Proceedings of the First Workshop on Fuzzy Based Expert Systems (pp. 53–55). Sofia, Bulgaria.

Shabani, A., & Baloui Jamkhaneh, E. (2014). A new generalized intuitionistic fuzzy number. Journal of Fuzzy Set Valued Analysis, 2014, 1–10. https://doi.org/10.5899/2014/jfsva-00199

Sari, I. U., & Kahraman, C. (2021). Intuitionistic fuzzy Z-numbers. In Intelligent and Fuzzy Techniques: Smart and Innovative Solutions (Advances in Intelligent Systems and Computing, Vol. 1197, pp. 1316–1324). Springer. https://doi.org/10.1007/978-3-030-51156-2_154

Uluçay, V., Deli, I., & Şahin, M. (2019). Intuitionistic trapezoidal fuzzy multi-numbers and its application to multi-criteria decision-making problems. Complex & Intelligent Systems, 5, 65–78. https://doi.org/10.1007/s40747-018-0074-z

Yang, X., Mahmood, T., Ali, Z., & Hayat, K. (2023). Identification and classification of multi-attribute decision-making based on complex intuitionistic fuzzy Frank aggregation operators. Mathematics, 11(15), 3292. https://doi.org/10.3390/math11153292

Du, Y., Du, X., Li, Y., Cui, J.-x., & Hou, F. (2022). Complex q-rung orthopair fuzzy Frank aggregation operators and their application to multi-attribute decision making. Soft Computing, 26(22), 11973–12008. https://doi.org/10.1007/s00500-022-07465-2

Ali, J., Naeem, M., & Al-Kenani, A. N. (2023). Complex T-spherical fuzzy Frank aggregation operators and their application to decision making. IEEE Access, 11, 88971–89023. https://doi.org/10.1109/ACCESS.2023.3298845

Mahmood, T., Waqas, H. M., Ali, Z., Ullah, K., & Pamucar, D. (2021). Frank aggregation operators and analytic hierarchy process based on interval-valued picture fuzzy sets and their applications. International Journal of Intelligent Systems, 36, 7925–7962. https://doi.org/10.1002/int.22614

Zhang, X., Liu, P., & Wang, Y. (2015). Multiple attribute group decision making methods based on intuitionistic fuzzy Frank power aggregation operators. Journal of Intelligent & Fuzzy Systems, 29(5), 2235–2246. https://doi.org/10.3233/IFS-151699

Qin, J., Liu, X., & Pedrycz, W. (2016). Frank aggregation operators and their application to hesitant fuzzy multiple attribute decision making. Applied Soft Computing, 41, 428–452. https://doi.org/10.1016/j.asoc.2015.12.030

Ullah, K., Naeem, M., Hussain, A., Waqas, M., et al. (2023). Evaluation of electric motor cars based Frank power aggregation operators under picture fuzzy information and a multi-attribute group decision-making process. IEEE Access, 11. https://doi.org/10.1109/ACCESS.2023.3285307

Zhou, H., et al. (2019). Two new approaches for multi-attribute group decision-making with interval-valued neutrosophic Frank aggregation operators and incomplete weights. IEEE Access, 7. https://doi.org/10.1109/ACCESS.2019.2927133

Wang, H., Mahmood, T., & Ullah, K. (2023). Improved CoCoSo method based on Frank softmax aggregation operators for T-spherical fuzzy multiple attribute group decision-making. International Journal of Fuzzy Systems, 25, 1275–1310. https://doi.org/10.1007/s40815-022-01442-5

Sarwar, M. A., Gong, Y., & Alzakari, S. A. (2026). q-Fractional fuzzy Frank aggregation operators and their application in decision-making. Fractal and Fractional, 10(3), 163. https://doi.org/10.3390/fractalfract10030163

Khan, A., Shah, A. A., & Abidin, M. Z. (2026). p, q, r-Fractional fuzzy Frank aggregation operators and their application in multi-criteria group decision-making. Fractal and Fractional, 10(1), 11. https://doi.org/10.3390/fractalfract10010011

Riaz, M., Farid, H. M. A., Wang, W., & Pamucar, D. (2022). Interval-valued linear Diophantine fuzzy Frank aggregation operators with multi-criteria decision-making. Mathematics, 10(11), 1811. https://doi.org/10.3390/math10111811

Khan, S., Abujabal, H. A., Rahim, M., Almutairi, A., Alburaikan, A., & Khalifa, H. A. E.-W. (2025). Multi attribute group decision-making based on quasirung orthopair fuzzy Frank aggregation operators for optimal vehicle selection. Scientific Reports, 15, 28868. https://doi.org/10.1038/s41598-025-12354-3

Madanchian, M., & Taherdoost, H. (2023). A comprehensive guide to the TOPSIS method for multi-criteria decision making. Sustainable Social Development, 1(1), 2220. https://doi.org/10.54517/ssd.v1i1.2220

Mitra, R., Das, J., & Kamruzzaman, M. M. (2023). Application of TOPSIS method for flood susceptibility mapping using Excel and GIS. MethodsX, 10, 102147. https://doi.org/10.1016/j.mex.2023.102147

Salsabeela, V., & John, S. J. (2021). TOPSIS techniques on Fermatean fuzzy soft sets. AIP Conference Proceedings, 2336, 040022. https://doi.org/10.1063/5.0045914

Ciardiello, F., & Genovese, A. (2023). A comparison between TOPSIS and SAW methods. Annals of Operations Research, 325, 967–994. https://doi.org/10.1007/s10479-023-05339-w

Akram, M., Dudek, W. A., & Ilyas, F. (2019). Group decision-making based on Pythagorean fuzzy TOPSIS method. International Journal of Intelligent Systems, 34(7), 1455–1475. https://doi.org/10.1002/int.22103

Chakraborty, S. (2022). TOPSIS and modified TOPSIS: A comparative analysis. Decision Analytics Journal, 2, 100021. https://doi.org/10.1016/j.dajour.2021.100021

Li, H., & Chen, L. (2022). Comprehensive evaluation model of coal mine safety under the combination of game theory and TOPSIS. Mathematical Problems in Engineering, 2022, Article 5623282. https://doi.org/10.1155/2022/5623282

Uzun, B., Mustapha, M. T., Syidanova, A., & Uzun Ozsahin, D. (2021). The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS). In Application of Multi-Criteria Decision Analysis in Environmental and Civil Engineering (pp. 25–30). Springer. https://doi.org/10.1007/978-3-030-64765-0_4

Zavadskas, E. K., Mardani, A., Turskis, Z., Jusoh, A., & Nor, K. M. (2016). Development of TOPSIS method to solve complicated decision-making problems—An overview on developments from 2000 to 2015. International Journal of Information Technology & Decision Making, 15(3), 645–682. https://doi.org/10.1142/S0219622016300019

Pan, X.-H., He, S.-F., Wang, Y.-M., & Martínez, L. (2022). A novel interval-valued three-way decision theory under multiple criteria environment. Knowledge-Based Systems, 259, 109522. https://doi.org/10.1016/j.knosys.2022.109522

Thakkar, J. J. (2021). Multi-criteria decision making (Studies in Systems, Decision and Control, Vol. 336). Springer. https://doi.org/10.1007/978-981-33-4745-8

Wang, Z., & Rangaiah, G. P. (2025). Chapter 8: Multi-criteria decision-making: Aggregation-type methods. arXiv preprint arXiv:2509.06388. https://doi.org/10.48550/arXiv.2509.06388

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Published

2026-10-04

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Vol. 2 No. 1 (2026): International Scientific Spectrum

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Articles

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Copyright (c) 2025 Muhammad Umar Mirza, Rabia Ali, Rukhshanda Anjum, Nasreen Kausar, Habiba Ramzan (Author)

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This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Mirza, M. U., Ali, R., Anjum, . R., Kausar, N., & Ramzan, H. (2026). Priorities for School Infrastructure Investment in the Face of Uncertainty: An Intuitionistic Fuzzy Multi-Criteria Decision-Making Method Employing the Frank Weighted Averaging Operator. International Scientific Spectrum, 2(1), 312-340. https://doi.org/10.66972/iscis21202624