Quarterly Publication

Document Type : Original Article


1 Department of Civil Engineering, Ayandegan Institute of Higher Education, Tonekabon, Iran.

2 Department of Applied Mathematics, Ayandegan Institute of Higher Education, Tonekabon, Iran.

3 Department of Management, Ayandegan Institute of Higher Education, Tonekabon, Iran.


Public-Private Partnership (PPP) refers to a partnership between a government and a private sector to provide public infrastructure projects, services, etc. These projects have been associated with numerous problems, many of which failed. A critical issue in PPP projects is choosing the right private-sector partner. Considering various criteria, the public sector has to select the best alternative concerning uncertainty. There needs to be a focus on well-structured, feasible decision approaches necessary to improve the performance of PPPs. In the MCDM context, the ratings of the alternatives provided by decision-makers can be expressed with the Fuzzy Set theory. Single-valued neutrosophic sets SVNSs are well suited for handling ambiguous, incomplete, and imprecise information. Moreover, some information measures for the SVNS model have been proposed, such as similarity measures. As selecting the suitable private-sector partner problem is an MCDM one, including various risk factors and uncertainty, this article has addressed choosing that by considering the risk factors as the problem criteria in a neutrosophic environment. We proposed a simple, practical approach to solve the problem of selecting the best private-sector partner. This approach considers the most critical risk factors affecting the infrastructure PPP project and copes with uncertainty using SVNSs.


  • Liang, Y., & Wang, H. (2019). Sustainable performance measurements for public–private partnership projects: empirical evidence from china. Sustainability, 11(13), 3653.‏ https://doi.org/10.3390/su11133653
  • Jiang, X., Lu, K., Xia, B., Liu, Y., & Cui, C. (2019). Identifying significant risks and analyzing risk relationship for construction PPP projects in china using integrated FISM-MICMAC approach. Sustainability, 11(19), 5206.‏ https://doi.org/10.3390/su11195206
  • Ahmadabadi, A. A., & Heravi, G. (2019). The effect of critical success factors on project success in public-private partnership projects: a case study of highway projects in Iran. Transport policy, 73, 152-161.‏ https://doi.org/10.1016/j.tranpol.2018.07.004
  • H., Valipour. A., Yahya. N., Noor. N. M., Beer. M., & Banaitiene. N. (2019). Approaches to risk identification in public–private partnership projects: malaysian private partners’ overview. Administrative sciences, 9(1), 17. https://doi:10.3390/admsci9010017
  • Faghihmaleki, H., Rahimireskati, S., & Darbandi, M. (2021). Value engineering and its impact on construction projects using building information modeling. Big data and computing visions, 1(2), 52-56.
  • R., & Dubey. A. M. (2019). Identification of critical success factors for public–private partnership projects. Journal of public affairs, 19(4), e1956. https://doi.org/10.1002/pa.1956
  • Loganathan, K., Najafi, M., Kaushal, V., & Agyemang, P. (2021). Evaluation of public private partnership in infrastructure projects. In Pipelines 2021 (pp. 151-159).‏ https://ascelibrary.org/doi/abs/10.1061/9780784483602.018
  • Guasch, j., Benitez. D., Portables. I., & Flor. L. (2014). The renegotiation of PPP contracts: an overview of its recent evolution in Latin America. International transport forum discussion paper, 18. OECD Publishing, Paris. https://doi.org/10.1787/5jrw2xxlks8v-en
  • Jokar, E., Aminnejad, B., & Lork, A. (2021). Assessing and prioritizing risks in public-private partnership (PPP) projects using the integration of fuzzy multi-criteria decision-making methods. Operations research perspectives8, 100190.‏ https://doi.org/10.1016/j.orp.2021.100190
  • Zhang, L., Sun, X., & Xue, H. (2019). Identifying critical risks in sponge city PPP projects using DEMATEL method: a case study of china. Journal of cleaner production226, 949-958.‏ https://doi.org/10.1016/j.jclepro.2019.04.067
  • Wu, Y., Song, Z., Li, L., & Xu, R. (2018). Risk management of public-private partnership charging infrastructure projects in China based on a three-dimension framework. Energy165, 1089-1101.‏ https://doi.org/10.1016/j.energy.2018.09.092
  • Y., Darko. A., Chan. A. P. C., Chen. C., & Bao. F. (2018). Evaluation and ranking of risk factors in transnational public private partnerships projects: case study based on the intuitionistic fuzzy analytic hierarchy process. Journal of infrastructure systems, 24(4), 04018028. https://doi.org/doi:10.1061/(ASCE)IS.1943-555X.0000448
  • Sorourkhah, A., Babaie-Kafaki, S., Azar, A., & Shafiei Nikabadi, M. (2019). A fuzzy-weighted approach to the problem of selecting the right strategy using the robustness analysis (case study: iran automotive industry). Fuzzy information and engineering11(1), 39-53.‏ https://doi.org/10.1080/16168658.2021.1886811
  • Sorourkhah, A., & Edalatpanah, S. A. (2022). Using a combination of matrix approach to robustness analysis (mara) and fuzzy DEMATEL-Based ANP (FDANP) to choose the best decision. International journal of mathematical, engineering and management sciences7(1), 68-80.‏ https://doi.org/10.33889/IJMEMS.2022.7.1.005
  • Rodríguez, R. M., Martínez, L., Torra, V., Xu, Z. S., & Herrera, F. (2014). Hesitant fuzzy sets: state of the art and future directions. International journal of intelligent systems29(6), 495-524.‏ https://10.1002/int.21654
  • Duran, V., Topal, S., & Smarandache, F. (2021). An application of neutrosophic logic in the confirmatory data analysis of the satisfaction with life scale. Journal of fuzzy extension and applications2(3), 262-282.‏
  • Rahman, A. U., Ahmad, M. R., Saeed, M., Ahsan, M., Arshad, M., & Ihsan, M. (2020). A study on fundamentals of refined intuitionistic fuzzy set with some properties. Journal of fuzzy extension and applications1(4), 279-292.‏ https://doi.org/10.22105/jfea.2020.261946.1067
  • A. (2022). Coping uncertainty in the supplier selection problem using a scenario-based approach and distance measure on type-2 intuitionistic fuzzy sets. Fuzzy optimization and modeling journal, 3(1), 64-71.
  • H., Smarandache. F., Zhang. Y., & Sunderraman. R. (2010). Single valued neutrosophic sets. Rev air force acad., 1(16), 10-14.
  • S. A. (2018). Neutrosophic perspective on DEA. Journal of applied research on industrial engineering, 5(4), 339-45. https://10.22105/jarie.2019.196020.1100
  • S. K., & Edalatpanah. S. A. (2020). A new ranking function of triangular neutrosophic number and its application in integer programming. International journal of neutrosophic science, 4(2), 82-92. https://doi.org/10.54216/IJNS.040202
  • M. R., Aghasi. S., & Davoodi. S. M. R. (2021). Ranking factors affecting supply chain risk with a combined approach of neutrosophic analytical hierarchy process and TOPSIS. Journal of applied research on industrial engineering. https://10.22105/jarie.2021.303869.1379
  • Smarandache, F., Broumi, S., Singh, P. K., Liu, C. F., Rao, V. V., Yang, H. L., ... & Elhassouny, A. (2019). Introduction to neutrosophy and neutrosophic environment. In Neutrosophic set in medical image analysis(pp. 3-29). Academic Press.
  • Şahin. R., & Liu. P. (2017). Correlation coefficients of single valued neutrosophic hesitant fuzzy sets and their applications in decision making. Neural computing and applications, 28(6), 1387-1395. https://10.1007/s00521-015-2163-x
  • M., & Krishnaswamy. M. (2020). K-algebras on quadripartitioned single valued neutrosophic sets. Journal of fuzzy extension and applications, 1(4), 325-339. https://10.22105/jfea.2020.254945.1026
  • Aydemir, S. B., & Kaya, T. (2021). TOPSIS method for multi-attribute group decision making based on neutrality aggregation operator under single valued neutrosophic environment: A case study of airline companies. In Neutrosophic operational research(pp. 471-492). Springer, Cham. https://doi.org/10.1007/978-3-030-57197-9_22
  • Garg, H. (2020). Algorithms for single-valued neutrosophic decision making based on TOPSIS and clustering methods with new distance measure. Infinite Study.
  • Abdullah, L., Ong, Z., & Mohd Mahali, S. (2021). Single-valued neutrosophic DEMATEL for segregating types of criteria: a case of subcontractors’ selection. Journal of mathematics2021. https://www.hindawi.com/journals/jmath/2021/6636029/
  • Chai, J. S., Selvachandran, G., Smarandache, F., Gerogiannis, V. C., Son, L. H., Bui, Q. T., & Vo, B. (2021). New similarity measures for single-valued neutrosophic sets with applications in pattern recognition and medical diagnosis problems. Complex & intelligent systems7(2), 703-723.‏ https://10.1007/s40747-020-00220-w
  • Deli, I. (2020). A New Multi-Attribute Decision-Making Method Based on Similarity Measures of SVTN-Numbers. In neutrosophic sets in decision analysis and operations research(pp. 59-81). IGI Global.‏ DOI: 4018/978-1-7998-2555-5.ch003
  • A., Azar. A., Babaie-Kafaki. S., & Shafiei. NikAbadi. M. (2017). Using weighted-robustness analysis in strategy selection (case study: saipa automotive research and innovation center). Industrial management journal, 9(4), 665-690. (In Persian). Https://10.22059/imj.2018.247856.1007361
  • F. (1998). Neutrosophy: neutrosophic probability, set, and logic: analytic synthesis & synthetic analysis: American Research Press.
  • Şahin, M., & Kargın, A. (2020). New similarity measure between single-valued neutrosophic sets and decision-making applications in professional proficiencies. In neutrosophic sets in decision analysis and operations research(pp. 129-149). IGI Global. DOI: 4018/978-1-7998-2555-5.ch007
  • Mishra, A. R., Rani, P., & Saha, A. (2021). Single‐valued neutrosophic similarity measure‐based additive ratio assessment framework for optimal site selection of electric vehicle charging station. International journal of intelligent systems36(10), 5573-5604.‏ https://doi.org/10.1002/int.22523
  • Yuan, J., Li, W., Guo, J., Zhao, X., & Skibniewski, M. J. (2018). Social risk factors of transportation PPP projects in China: A sustainable development perspective. International journal of environmental research and public health15(7), 1323. https://doi:10.3390/ijerph15071323
  • Cui, C., Liu, Y., Hope, A., & Wang, J. (2018). Review of studies on the public–private partnerships (PPP) for infrastructure projects. International journal of project management36(5), 773-794.‏ https://doi.org/10.1016/j.ijproman.2018.03.004
  • Valipour, A., Sarvari, H., & Tamošaitiene, J. (2018). Risk assessment in PPP projects by applying different MCDM methods and comparative results analysis. Administrative sciences8(4), 80.‏ https://doi.org/10.3390/admsci8040080
  • Sorourkhah, A., & Edalatpanah, S. A. (2021). Considering the criteria interdependency in the matrix approach to robustness analysis with applying fuzzy ANP. Fuzzy optimization and modeling journal2(2), 22-33‏. DOI: 30495/FOMJ.2021.1932066.1029
  • Sorourkhah, A., Babaie-Kafaki, S., Azar, A., & Shafiei-Nikabadi, M. (2018). Matrix‎ a‎ pproach to‎ r‎ obustness‎ a‎ nalysis for‎ s‎ trategy‎ s‎International journal of industrial mathematics10(3), 261-269. https://ijim.srbiau.ac.ir/article_12651.html
  • Mahapatra, N. K., & Bera, T. (2020). Generalised Single-Valued Neutrosophic Number and Its Application to Neutrosophic Linear Programming. In Neutrosophic sets in decision analysis and operations research(pp. 180-214). IGI Global.‏ DOI: 4018/978-1-7998-2555-5.ch009
  • Edalatpanah, S. A. (2020). Neutrosophic structured element. Expert systems, 37(5), e12542. https://doi.org/10.1111/exsy.12542
  • Ye, J. (2015). Multiple-attribute decision-making method under a single-valued neutrosophic hesitant fuzzy environment. Journal of intelligent systems24(1), 23-36.‏ https://doi:10.1515/jisys-2014-0001
  • Zhang, K., Xie, Y., Noorkhah, S. A., Imeni, M., & Das, S. K. (2022). Neutrosophic management evaluation of insurance companies by a hybrid TODIM-BSC method: a case study in private insurance companies. Management decision. https://doi.org/10.1108/MD-01-2022-0120