Interval fuzzy AHP method in risk assessment


  • Darko Bozanic University of Defense in Belgrade, Military Academy, Serbia
  • Duško Tešić Military Academy, University of Defence in Belgrade, Belgrade, Serbia
  • Nenad Komazec Military Academy, University of Defence in Belgrade, Belgrade, Serbia
  • Dragan Marinković TU Berlin, Department of Structural Analysis, Berlin, Germany
  • Adis Puška Department of Public Safety, Government of Brčko District of Bosnia and Herzegovina, Brčko, Bosnia and Herzegovina



Interval fuzzy number , AHP method, MCDM, Floods


The Analytic Hierarchy Process (AHP) method is one of the oldest and mostly used multi-criteria decision-making methods. In addition to the development of a large number of other methods, the AHP method is still widely applied. More and more often, this method is being modified by the application of various mathematical tools dealing with the consideration of uncertainty and indeterminacy. This paper presents an approach to the modification of the AHP method using triangular interval fuzzy numbers. In this approach, the confidence interval of the fuzzy number describing the comparison of criteria differs from one comparison to another. It depends on the opinion of the decision makers/experts, respectively, on their certainty in the comparison they make. The modification of the method is presented on the problem of selecting the course of navigation of vessels in flooded areas, based on the risk assessment of each predicted course.



Ali, A., Ullah, K., & Hussain, A. (2023). An approach to multi-attribute decision-making based on intuitionistic fuzzy soft information and Aczel-Alsina operational laws. Journal of Decision Analytics and Intelligent Computing, 3(1), 80-89.

Ayyildiz, E., & Taskin Gumus, A. (2021). Pythagorean fuzzy AHP based risk assessment methodology for hazardous material transportation: an application in Istanbul. Environmental Science and Pollution Research, 28, 35798-35810.

Badi, I., Stević, Ž., & Bayane Bouraima, M. (2023). Overcoming Obstacles to Renewable Energy Development in Libya: An MCDM Approach towards Effective Strategy Formulation. Decision Making Advances, 1(1), 17-24.

Ban, A. I., Ban, O. I., Bogdan, V., Popa, D. C. S., & Tuse, D. (2020). Performance evaluation model of Romanian manufacturing listed companies by fuzzy AHP and TOPSIS. Technological and Economic Development of Economy, 26(4), 808-836.

Bhatt, N., Guru, S., Thanki, S., & Sood, G. (2021). Analysing the factors affecting the selection of ERP package: A fuzzy AHP approach. Information Systems and e-Business Management, 19, 641-682.

Bitarafan, M., Amini Hosseini, K., & Zolfani, S. H. (2023). Identification and assessment of man-made threats to cities using integrated Grey BWM- Grey MARCOS method. Decision Making: Applications in Management and Engineering, 6(2), 581–599.

Boral, S., Howard, I., Chaturvedi, S. K., McKee, K., & Naikan, V. N. A. (2020). An integrated approach for fuzzy failure modes and effects analysis using fuzzy AHP and fuzzy MAIRCA. Engineering Failure Analysis, 108, 104195.

Bošković, S., Radonjić-Djogatović, V., Ralević, P., Dobrodolac, M., & Jovčić, S. (2021). Selection of mobile network operator using the CRITIC-ARAS method. International Journal for Traffic & Transport Engineering, 11(1), 17-29.

Bošković, S., Švadlenka, L., Dobrodolac, M., Jovčić, S., & Zanne, M. (2023). An Extended AROMAN Method for Cargo Bike Delivery Concept Selection. Decision Making Advances, 1(1), 1-9.

Božanić, D., Pamučar, D., & Karović, S. (2016a). Use of the fuzzy AHP - MABAC hybrid model in ranking potential locations for preparing laying-up positions. Military Technical Courier, 64 (3), 705-729.

Božanić, D., Pamučar, D., & Komazec, N. (2016b). Application of the fuzzy AHP method in Risk Assessment in the selection of navigation vehicles directions of Serbian Army in flooded areas. In Proceedings of the Security and Crisis Management - Theory and Practice (SeCMan) (pp. 39-46), Obrenovac, Serbia.

Božanić, D., Slavković, R., & Karović, S. (2015). Model of fuzzy logic application to the assessment of risk in overcoming the water obstacles durin an army defensive operation. Vojno delo, 67(4), 240-260.

Büyüközkan, G., Havle, C. A., & Feyzioğlu, O. (2021). An integrated SWOT based fuzzy AHP and fuzzy MARCOS methodology for digital transformation strategy analysis in airline industry. Journal of Air Transport Management, 97, 102142.

Çalık, A. (2021). A novel Pythagorean fuzzy AHP and fuzzy TOPSIS methodology for green supplier selection in the Industry 4.0 era. Soft Computing, 25(3), 2253-2265.

Castillo, O., & Melin, P. (2008). Type-2 Fuzzy Logic: Theory and Applications. Heidelberg: Springer.

Coffey, L., & Claudio, D. (2021). In defense of group fuzzy AHP: A comparison of group fuzzy AHP and group AHP with confidence intervals. Expert Systems with Applications, 178, 114970.

Debnath, S., & Ghosh, S. (2021). Experimental investigation of Electro discharge machining process by AHP-MOORA technique. Journal of Industrial Engineering and Decision Making, 2(1), 1-7.

Đukić, Đ., Petrović, I., Božanić, D, & Delibašić, B. (2022). Selection of Unployed Aircraft for Training of Small-Range Aircraft Defense System AHP – TOPSIS Optimization Methods. Yugoslav Journal of Operations Research, 32(3), 389-406.

Durmić, E., Stević, Ž., Chatterjee, P., Vasiljević, M., & Tomašević, M. (2020). Sustainable supplier selection using combined FUCOM – Rough SAW model. Reports in Mechanical Engineering, 1(1), pp. 34-43.

FM 5-19 Composite Risk Management. (2006). Washington DC: Headquarters Department of the Army.

Granados, C., Das, A. K., & Osu, B. O. (2022). Weighted Neutrosophic Soft Multiset and Its Application to Decision Making. Yugoslav Journal of Operations Research, 33(2), 293-308.

Hossain, M. K., & Thakur, V. (2021). Benchmarking health-care supply chain by implementing Industry 4.0: a fuzzy-AHP-DEMATEL approach. Benchmarking: An International Journal, 28(2), 556-581.

Iphar, M., & Cukurluoz, A. K. (2020). Fuzzy risk assessment for mechanized underground coal mines in Turkey. International journal of occupational safety and ergonomics, 26(2), 256-271.

John, A., Paraskevadakis, D., Bury, A., Yang, Z., & Riahi, R. (2014). An integrated fuzzy risk assessment for seaport operations. Safety Science, 68, 180-194.

Jumaryadi, Y., Firdaus, D., Priambodo, B., & Putra, Z. P. (2020). Determining the best graduation using fuzzy AHP. In Proceedings of the 2nd International Conference on Broadband Communications, Wireless Sensors and Powering (BCWSP) (pp. 59-63). IEEE.

Kahraman, C., Onar, S. C., Öztayşi, B., Şeker, Ş., & Karaşan, A. L. I. (2020). Integration of fuzzy AHP with other fuzzy multicriteria methods: A state of the art survey. Journal of Multiple-Valued Logic & Soft Computing, 35, 61-92.

Kahraman, C., Öztayşi, B., Uçal, S. I., & Turanoğlu, E. (2014). Fuzzy analytic hierarchy process with interval type-2 fuzzy sets. Knowledge-Based Systems, 59, 48-57.

Khodadadi-Karimvand, M., & Shirouyehzad, H. (2021). Well drilling fuzzy risk assessment using fuzzy FMEA and fuzzy TOPSIS. Journal of fuzzy extension and applications, 2(2), 144-155.

Koohathongsumrit, N., & Meethom, W. (2021). An integrated approach of fuzzy risk assessment model and data envelopment analysis for route selection in multimodal transportation networks. Expert Systems with Applications, 171, 114342.

Kozhukhivskyi, A. D., & Kozhukhivska, O. A. (2022). Developing a fuzzy risk assessment model for erpsystems. Radio Electronics, Computer Science, Control, (1), 106-106.

Lin, S. S., Shen, S. L., Zhou, A., & Xu, Y. S. (2021). Risk assessment and management of excavation system based on fuzzy set theory and machine learning methods. Automation in Construction, 122, 103490.

Lyu, H. M., Sun, W. J., Shen, S. L., & Zhou, A. N. (2020). Risk assessment using a new consulting process in fuzzy AHP. Journal of Construction Engineering and Management, 146(3), 04019112.

Mendoza, O., Melin, P., & Licea, G. (2009). A hybrid approach for image recognition combining type-2 fuzzy logic, modular neural networks and the Sugeno integral. Journal of Information Sciences, 179(13), 2078-2101.

Milićević, M. (2014). Experts' assessment (Only in Serbian: Ekspertsko ocenjivanje). Belgrade: Odbrana Media Center.

Milovanović, V. R., Aleksić, A. V., Sokolović, V. S., & Milenkov, M. A. (2021). Uncertainty modeling using intuitionistic fuzzy numbers. Military Technical Courier, 69(4), 905-929.

Nazim, M., Mohammad, C. W., & Sadiq, M. (2022). A comparison between fuzzy AHP and fuzzy TOPSIS methods to software requirements selection. Alexandria Engineering Journal, 61(12), 10851-10870.

Pamucar, D., & Görçün, Ö. F. (2022). Evaluation of the European container ports using a new hybrid fuzzy LBWA-CoCoSo'B techniques. Expert Systems with Applications, 203, 117463.

Pamučar, D., Lukovac, V., & Božanić, D. (2015). Creating a portfolio matrix for the analysis of the human resources using a fuzzy logic system (Only in Serbian: Izrada portfolio matrice za analizu ljudskih resursa primenom fuzzy logičkog sistema tip-2). In Proceedings of the SYM-OP-IS-2015 (pp. 478-481), Silver Lake, Serbia.

Pamucar, D., Simic, V., Lazarević, D., Dobrodolac, M., & Deveci, M. (2022). Prioritization of sustainable mobility sharing systems using integrated fuzzy DIBR and fuzzy-rough EDAS model. Sustainable Cities and Society, 82, 103910.

Pamučar, D., Žižović, M., Biswas, S., & Božanić, D. (2021). A new Logarithm Methodology of Additive Weights (LMAW) for multi-criteria decision-making: Application in logistics. Facta Universitatis, Series: Mechanical Engineering, 19(3), 361-380.

Puška, A., Štilić, A., & Stojanović, I. (2023). Approach for multi-criteria ranking of Balkan countries based on the index of economic freedom. Journal of Decision Analytics and Intelligent Computing, 3(1), 1-14.

Rajabpour, E., Fathi, M. R., & Torabi, M. (2022). Analysis of factors affecting the implementation of green human resource management using a hybrid fuzzy AHP and type-2 fuzzy DEMATEL approach. Environmental Science and Pollution Research, 29(32), 48720-48735.

Saaty, T. L. (1980). The analytic hierarchy process. New York: McGraw-Hill.

Si, A., & Ganguly, U. (2021). Drainage and management of offseason rain water in multipurpose reservoir using fuzzy model. Journal of Industrial Engineering and Decision Making, 2(1), 22-26.

Sivaprakasam, P., & Angamuthu, M. (2023). Generalized Z-fuzzy soft β-covering based rough matrices and its application to MAGDM problem based on AHP method. Decision Making: Applications in Management and Engineering, 6(1), 134–152.

Tešić, D. Z., Božanić, D. I., Pamučar, D. S., & Din, J. (2022a). DIBR - Fuzzy MARCOS model for selecting a location for a heavy mechanized bridge. Military technical courier, 70(2), 314-339.

Tešić, D., Radovanović, M., Božanić, D., Pamučar, D., Milić, A., & Puška, A. (2022b). Modification of the DIBR and MABAC Methods by Applying Rough Numbers and Its Application in Making Decisions. Information, 13(8), 353.

Topal, S., & Atasoylu, E. (2022). A Fuzzy Risk Assessment Model for Small Scale Construction Work. Sustainability, 14(8), 4442.

Tripathi, A. K., Agrawal, S., & Gupta, R. D. (2021). Comparison of GIS-based AHP and fuzzy AHP methods for hospital site selection: a case study for Prayagraj City, India. GeoJournal, 1-22.

Wang, X., Zhang, C., Wang, C., Zhu, Y., & Cui, Y. (2021). Probabilistic-fuzzy risk assessment and source analysis of heavy metals in soil considering uncertainty: A case study of Jinling Reservoir in China. Ecotoxicology and Environmental Safety, 222, 112537.

Wang, Y., Xu, L., & Solangi, Y. A. (2020). Strategic renewable energy resources selection for Pakistan: Based on SWOT-Fuzzy AHP approach. Sustainable Cities and Society, 52, 101861.

Yucesan, M., & Gul, M. (2020). Hospital service quality evaluation: an integrated model based on Pythagorean fuzzy AHP and fuzzy TOPSIS. Soft Computing, 24(5), 3237-3255.

Zhou, B., Chen, J., Wu, Q., Pamučar, D., Wang, W., & Zhou, L. (2022). Risk priority evaluation of power transformer parts based on hybrid FMEA framework under hesitant fuzzy environment. Facta Universitatis, Series: Mechanical Engineering, 20(2), 399-420.



How to Cite

Bozanic, D., Tešić, D., Komazec, N., Marinković, D., & Puška, A. (2023). Interval fuzzy AHP method in risk assessment . Reports in Mechanical Engineering, 4(1), 131–140.