Application of the Fuzzy DIBR II–MABAC Model in the Selection of Position Area and Target

Aleksandar Aleksić; Zeljko Jokić; Stefan Tošić; Miša Živković; Damir Jerković

doi:10.65069/smart2120268

Authors

Aleksandar Aleksić Military Academy, University of Defence in Belgrade Author https://orcid.org/0000-0003-1103-8410
Zeljko Jokić Military Academy, University of Defence in Belgrade Author https://orcid.org/0000-0002-3646-1787
Stefan Tošić Military Academy, University of Defence in Belgrade Author https://orcid.org/0009-0001-1003-2044
Miša Živković Military Academy, University of Defence in Belgrade Author https://orcid.org/0009-0007-1918-4259
Damir Jerković Military Academy, University of Defence in Belgrade Author https://orcid.org/0000-0001-5182-7057

DOI:

https://doi.org/10.65069/smart2120268

Keywords:

Fuzzy DIBR II–MABAC, fire position, target

Abstract

The paper introduces a hybrid decision-making model that integrates the fuzzy Defining Interrelationships Between Ranked Criteria II (fuzzy DIBR II) and fuzzy Multi-Attributive Border Approximation Area Comparison (fuzzy MABAC) methods to determine the optimal initial and final projectile positions for maximizing operational effectiveness. Evaluation criteria were established by experts in Military Sciences. The DIBR II method was applied to calculate the criteria weighting coefficients. Crisp values are appropriate when uncertainty is low and input parameters are clearly defined, whereas fuzzy values are more suitable in contexts characterized by higher uncertainty. Given the numerous uncertain factors in the problem under consideration, the use of fuzzy numbers is well justified. The fuzzy MABAC method was subsequently employed to rank four feasible alternatives and identify the most favorable projectile positions.

To assess the robustness of the proposed model, a sensitivity analysis was conducted by varying the values of the criterion with the highest weighting coefficient. In addition, a comparative analysis was performed by individually modifying the criteria values for each alternative, with the resulting rankings compared against the initial outcomes. The model consistently identified alternative A3, associated with steep terrain, as the optimal solution, thereby demonstrating its reliability in supporting the selection of projectile positions under conditions of uncertainty.

References

[1] Biletskyi, V., Tyshchuk, V., & Mandziuk, O. (2026). Autonomous Systems and the Speed of Battle: Legal Risks and Strategic Adaptation in AI-Enabled Warfare. Scandinavian Journal of Military Studies, 9(1), 210-224. https://doi.org/10.31374/sjms.441.

[2] Glišin, V., & Petrović, J. (2025). The Use of Unmanned Aerial Vehicles for Military Purposes – A Global Perspective on the Development of Technology. America’s Unilateral Shift: the Evolution of Us Foreign Policy From Liberal Hegemony to a Rogue Superpower, 76(1195), 399-420. https://doi.org/10.18485/iipe_ria.2025.76.1195.2.

[3] Drábek, J., Šustr, M., Potužák, L., Ivan, J., & Liška, R. (2025). Contingency and Emergency Manual Procedures for Calculation Firing Data Using Direction and Distance Coefficients. Engineering Reports, 7(6), e70252. https://doi.org/10.1002/eng2.70252.

[4] Mosser, J. (2025). When Armour Can’t Support Infantry. The RUSI Journal, 170(3), 28-39. https://doi.org/10.1080/03071847.2025.2499478.

[5] Rulebook for the 30 mm M93 Automatic Grenade Launcher. (2021). Infantry Directorate, General Staff of the Yugoslav Army.

[6] Zhao, L., Wang, B., Chen, P., & Sun, J. (2025). Optimization Methods for Air-to-Ground Weapon-Target Assignment Problems Based on Multi-Agent Dynamic Game Theory. In 2025 Asian Conference on Artificial Intelligence Technology (ACAIT) (pp. 1026-1036). IEEE. https://doi.org/10.1109/ACAIT67930.2025.11521912.

[7] Božanić, D. I., & Pamučar, D. S. (2010). Evaluating locations for river crossing using fuzzy logic. Vojnotehnički glasnik/Military Technical Courier, 58(1), 129-145. https://doi.org/10.5937/vojtehg1001129B.

[8] Pamučar, D., Božanić, D. & Milić, A. (2016). Selection of a course of action by Obstacle Employment Group based on a fuzzy logic system, Yugoslav Journal of Operations Research, 26(1), 75-90. https://doi.org/ 10.2298/YJOR140211018P.

[9] Sennaroglu, B. & Celebi, G. V. (2018). A military airport location selection by AHP integrated PROMETHEE and VIKOR methods, Transportation Research Part D: Transport and Environment, Volume 59, 160-173. https://doi.org/10.1016/j.trd.2017.12.022.

[10] Pamučar, D., & Božanić, D. (2019). Selection of a location for the development of multimodal logistics center: Application of single-valued neutrosophic MABAC model, Operational Research in Engineering Sciences: Theory and Applications, 2(2), 55-71. https://doi.org/10.31181/oresta1902039p.

[11] Karatas, M., Yakici, E. & Razi, N. (2019). Military Facility Location Problems: A Brief Survey, Operations Research for Military Organizations, 1-27. https://doi.org/10.4018/978-1-5225-5513-1.ch001.

[12] Radovanović, M., Ranđelović, A. & Jokić, Ž. (2020). Application of hybrid model fuzzy AHP - VIKOR in selection of the most efficient procedure for rectification of the optical sight of the longrange rifle, Decision Making: Applications in Management and Engineering Vol. 3, Issue 2, 131-148. https://doi.org/10.31181/dmame2003131r.

[13] Petrović, I. & Kankaraš, М. (2020). A Hybridized IT2FS-DEMATEL-AHP-TOPSIS Multi-Criteria Decision Making Approach: Case Study of Selection and Evaluation of Criteria for Determination of Air Traffic Control Radar Position, Decision Making: Applications in Management and Engineering, 146-164. https://doi.org/10.31181/dmame200301P.

[14] Hamurcu, M. & Eren, T. (2019). An Application of Multicriteria Decision-making for the Evaluation of Alternative Monorail Routes, Mathematics, 7, 16. https://doi.org/10.3390/ math7010016.

[15] Stoilova, S. (2020). An Integrated Multi-Criteria Approach for Planning Railway Passenger Transport in the Case of Uncertainty, Symmetry, 12, 949. https://doi.org/10.3390/sym12060949.

[16] Liang, Y., Liu, F., Lim, A. & Zhang, D. (2020). An integrated route, temperature and humidity planning problem for the distribution of perishable products, Computers & Industrial Engineering, 147:106623, https://doi.org/10.1016/j.cie.2020.106623.

[17] Xu, X., Grace Guo, W. & Rodgers, M. D. (2020). A real-time decision support framework to mitigate degradation in perishable supply chains, Computers & Industrial Engineering, 150. https://doi.org/10.1016/j.cie.2020.106905.

[18] Mihajlović, J., Rajković, P., Petrović, G. & Ćirić, D. (2019). The Selection of the Logistics Distribution Center Location Based on MCDM Methodology in Southern and Eastern Region in Serbia, Operational Research in Engineering Sciences: Theory and Applications, 2(2), 72-85. https://doi.org/10.31181/oresta190247m.

[19] Küçükaydın, H. & Aras, N. (2020). Gradual covering location problem with multi-type facilities considering customer preferences, Computers & Industrial Engineering, 147:106577. https://doi.org/10.1016/j.cie.2020.106577.

[20] Contreras I., & O’Kelly M. (2019). Hub Location Problems. In: Laporte G., Nickel S., Saldanha da Gama F. (eds) Location Science. Springer, Cham. https://doi.org/10.1007/978-3-030-32177-2_12.

[21] Pan Y., Zhang, L., Koh, J. & Deng, Y. (2021). An adaptive decision making method with copula Bayesian network for location selection, Information Sciences, Volume 544, 56-77. https://doi.org/10.1016/j.ins.2020.07.063.

[22] Kouaied, A., Msaddek, M. H., Zghibi, A., Barrek, A., Pistre, S., & Chenini, I. (2025). Groundwater Recharge zone mapping in a Coastal Mediterranean Aquifer applying Fuzzy and Analytical Hierarchy Process and frequency ratio: A Case Study of northeast Tunisia. Journal of African Earth Sciences, 105537. https://doi.org/10.1016/j.jafrearsci.2025.105537.

[23] Jokić, Ž., Božanić, D., & Pamučar, D. (2021). Selection of fire position of mortar units using LBWA and Fuzzy MABAC model. Operational Research in Engineering Sciences: Theory and Applications, 4(1), 115-135. https://doi.org/10.31181/oresta20401156j.

[24] Pamucar, D., Deveci, M., Gokasar, I., Işik, M. & Zizovic, M. (2021). Circular economy concepts in urban mobility alternatives using integrated DIBR method and fuzzy Dombi CoCoSo model. Journal of Cleaner Production, 323, 129096. https://doi.org/10.1016/j.jclepro.2021.129096.

[25] Tešić, D., Božanić, D. & Khalilzadeh, M. (2024). Enhancing Multi-Criteria Decision-Making with Fuzzy Logic: An Advanced Defining Interrelationships Between Ranked II Method Incorporating Triangular Fuzzy Numbers. Journal of Intelligent Management Decision, 3(1), 56-67. https://doi.org/10.56578/jimd030105.

[26] Nila, B., Pamucar, D., & Roy, J. (2024). Designing and analyzing drone-based city logistics solutions for Kochi using a Fuzzy Multi-Criteria decision making framework. Environment, Development and Sustainability, 1-36. https://doi.org/10.1007/s10668-024-05867-w.

[27] Moskolaï Ngossaha, J., Fonkoua Tatang, K. N., & Ntjam Ngamby, L. B. (2024). Integrating fuzzy multicriteria decision making approach for improving the quality of urban mobility services in developing countries. Journal of Infrastructure, Policy and Development, 8(8), 6183. https://doi.org/10.24294/jipd.v8i8.6183.

[28] Eti, S., & Yüksel, S. (2024). Integrating pythagorean fuzzy SAW and ENTROPY in decision-making for legal effectiveness in renewable energy projects: Legal effectiveness in renewable energy projects. Computer and Decision Making: An International Journal, 1, 13-22. https://doi.org/10.59543/comdem.v1i.10043.

[29] Dağıstanlı, H. A. (2025). Weapon System Selection for Capability-Based Defense Planning using Lanchester Models integrated with Fuzzy MCDM in Computer Assisted Military Experiment. Knowledge and Decision Systems with Applications, 1, 11-23. https://doi.org/10.59543/kadsa.v1i.13601.

[30] Božanić, D., Borota, M., Štilić, A., Puška, A., & Milić, A. (2024). Fuzzy DIBR II-MABAC model for flood prevention: A case study of the river Veliki Rzav. Journal of Decision Analytics and Intelligent Computing, 4(1), 285-298. https://doi.org/10.31181/jdaic10031122024b.

[31] Ayvaz, B., Tatar, V., Sağır, Z. & Pamučar, D. (2024). An integrated Fine-Kinney risk assessment model utilizing Fermatean fuzzy AHP-WASPAS for occupational hazards in the aquaculture sector. Process Safety and Environmental Protection, 186, 232-251. https://doi.org/10.1016/j.psep.2024.04.025.

[32] Ali, S. I., Lalji, S. M., Haider, S. A., Haneef, J., Husain, N., Yahya, A., ... & Arfeen, Z. A. (2024). Risk prioritization in a core preparation experiment using fuzzy VIKOR integrated with Shannon entropy method. Ain Shams Engineering Journal, 15(2), 102421. https://doi.org/10.1016/j.asej.2023.102421.

[33] Biswas, A., Gazi, K. H., Bhaduri, P., & Mondal, S. P. (2024). Neutrosophic fuzzy decision-making framework for site selection. Journal of Decision Analytics and Intelligent Computing, 4(1), 187–215. https://doi.org/10.31181/jdaic10004122024b.

[34] Žnidaršič, V., Dojić,, K.V. & Milić, N. L. (2024). Selection of Landing Site for Infantry River Crossing Using Aluminum Boat M70: Application of DIBR and Topsis Method. International conference KNOWLEDGE-BASED ORGANIZATION, 2024, 1, 193-200. https://doi.org/10.2478/kbo-2024-0027.

[35] Božanić, D., Puška, A., Tešić, D., Štilić, A., Ullah, K., Muhsen, Y., R., & Ibrahim M. Hezam. (2025). Fuzzy AHP-Fuzzy MABAC Model for ranking a Combined Construction Machine-Backhoe Loader, Facta Universitatis, Series: Mechanical Engineering, 23(3), 605-625. https://doi.org/10.22190/FUME250801030B.

[36] Božanić, D. & Pamučar, D. (2023). Overview of the Method Defining Interrelationships Between Ranked Criteria II and Its Application in Multi-criteria Decision-Making. In: Chatterjee, P., Pamucar, D., Yazdani, M., Panchal, D. (eds) Computational Intelligence for Engineering and Management Applications. Lecture Notes in Electrical Engineering, 984. Springer, Singapore. https://doi.org/10.1007/978-981-19-8493-8_64.

[37] Tešić, D., & Marinković, D. (2023). Application of fermatean fuzzy weight operators and MCDM model DIBR-DIBR II-NWBM-BM for efficiency-based selection of a complex combat system. Journal of Decision Analytics and Intelligent Computing, 3(1), 243–256. https://doi.org/10.31181/10002122023t.

[38] Radovanović, M., Živković, M., & Crnogorac, M. (2025). Application of Decision-Making Support Model in the Operations Planning Process at the Tactical Level. Vojenské rozhledy, 106(1), 85-103. https://doi.org/10.3849/2336-2995.34.2025.01.085-103.

[39] Chatterjee, P. & Stević, Ž. (2019). A two-phase fuzzy AHP-fuzzy TOPSIS model for supplier evaluation in manufacturing environment, Operational Research in Engineering Sciences: Theory and Applications, 2(1), 72-90. Available at: https://oresta.org/menu-script/index.php/oresta/article/view/19/16.

[40] Bojadziev, G. & Bojadziev, M. (1996). Fuzzy sets and fuzzy logic applications, World Scientific. ISBN 9810226063.

[41] Zimmermann, H.J. (1998). Fuzzy Set Theory and Its Applications, Kluwer, Boston. https://doi.org/10.1007/978-94-010-0646-0.

[42] Zadeh, Lotfi A. (1965). Fuzzy sets, Information and control 8.3, 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X.

[43] Kwong, C. K. & Bai, H. (2003). Determining the importance weights for the customer requirements in QFD using a fuzzy AHP with an extent analysis approach, Iie Transactions, 35(7), 619-626. https://doi.org/10.1080/07408170304355.

[44] Pamučar, D. & Ćirović, G. (2015). The selection of transport and handling resources in logistics centres using Multi Attributive Border Approximation area Comparison (MABAC), Expert Systems with Applications, 42(6), 3016-3028. https://doi.org/10.1016/j.eswa.2014.11.057.

[45] Alinezhad, A. & Khalili, J. (2019). MABAC Method. In: New Methods and Applications in Multiple Attribute Decision Making (MADM), International Series in Operations Research & Management Science, 277. https://doi.org/10.1007/978-3-030-15009-9_25.

[46] Sun, R., Hu, J., Zhou., J. & Chen. X. (2017). A Hesitant Fuzzy Linguistic Projection-Based MABAC Method for Patients’ Prioritization, International Journal of Fuzzy Systems, 20, 2144–2160. https://doi.org/10.1007/s40815-017-0345-7.

[47] Sharma, K., H., Roy, J., Kar, S., & Prentkovskis, O. (2018). Multi Criteria Evaluation Framework for Prioritizing Indian Railway Stations Using Modified Rough AHP-MABAC Method, Transport and Telecommunication Journal, 19(2), 113-127. https://doi.org/10.2478/ttj-2018-0010.

[48] Wang, J., Wei, G., Wei, C., & Wei, Y. (2020). MABAC method for multiple attribute group decision making under q-rung orthopair fuzzy environment, Defence Technology, 16(1), 208-216. https://doi.org/10.1016/j.dt.2019.06.019.

[49] Liang, W., Zhao, G., Wu, H. & Dai, B. (2019). Risk assessment of rockburst via an extended MABAC method under fuzzy environment, Tunnelling and Underground Space Technology, 83, 533-544. https://doi.org/10.1016/j.tust.2018.09.037.

[50] Luo, S-z., Wei-zhang Liang, W-z. (2019). Optimization of roadway support schemes with likelihood-based MABAC method, Applied Soft Computing, 80, 80-92. https://doi.org/10.1016/j.asoc.2019.03.020.

[51] Mishra, A.R., Chandel, A. & Motwani, D. (2020). Extended MABAC method based on divergence measures for multi-criteria assessment of programming language with interval-valued intuitionistic fuzzy sets, Granular Computing, 5, 97-117. https://doi.org/10.1007/s41066-018-0130-5.

[52] Sahoo, B., & Debnath, B. K. (2024). Select the best place for regenerative practices in tourism by using the fuzzy MABAC method. In Building Community Resiliency and Sustainability With Tourism Development, 261-285. https://doi.org/10.4018/979-8-3693-5405-6.ch012.

[53] Božanic, D., Tešić, D., & Milićević, J. (2018). A hybrid fuzzy AHP-MABAC model: Application in the Serbian Army – The selection of the location for deep wading as a technique of crossing the river by tanks. Decision Making: Applications in Management and Engineering, 1(1), 143–164. https://doi.org/10.31181/dmame1801143b.

[54] Pamučar, D., Petrović, I. & Ćirović, G. (2018). Modification of the Best–Worst and MABAC methods: A novel approach based on interval-valued fuzzy-rough numbers, Expert Systems with Applications, 91, 89-106. https://doi.org/10.1016/j.eswa.2017.08.042.

[55] Krtolica, N., Stojanovic, V., Crnkovic, M., Dragutinovic, M., & Markovic, N. (2002). Manual for Tactical Training. General Staff of the Yugoslav Army.

[56] U.S. Army. (2026). ATP 3-21.50: Decentralized small-unit operations in mountainous terrain. Department of the Army. Available at: ia803100.us.archive.org/24/items/DTIC_ADA546519/DTIC_ADA546519.pdf.

[57] Angelidou, C., Chambers, V., Hobbs, B., Karakasis, C., & Artemiadis, P. (2025). Kinematics, kinetics, and muscle activations during human locomotion over compliant terrains. Scientific Data, 12(1), 84. https://doi.org/10.1038/s41597-025-04433-x.

[58] Potić, I., & Đorđević, D. (2025). Terrain Passability Modeling for Cross‐Country Unmanned Ground Vehicle Navigation. Transactions in GIS, 29(2), e70035. https://doi.org/10.1111/tgis.70035.

[59] U.S. Army. (2025). ATP 3-21.8: Infantry platoon and squad. Department of the Army. Available at: https://www.battleorder.org/post/atp3-21-8.

[60] Ryzhonkova, N. V., Beskostova, A. A., Danchenkov, D. V., & Solodukhin, A. V. (2023). Practical skills of terrain orientation as the basis for analyzing and assessing the tactical properties of terrain in the process of military-topographic training of servicemen and law enforcement personnel (in Russian: Практические навыки ориентирования на местности как основа анализа и оценки тактических свойств местности в процессе военно-топографической подготовки военнослужащих и сотрудников силовых ведомств). Lesgaft University Scientific Notes, 6 (220), 340–344. Available at: https://uchzapiski.lesgaft.spb.ru/ru/storage/download/275648.

[61] Tešić, D., Radovanović, M., Božanić, D. Pamučar, D., Milić, A. & Puška, A. (2022). Modification of the DIBR and MABAC methods by applying rough numbers and its application in making decisions, Information, 13(8), 353. https://doi.org/10.3390/info13080353.

[62] Božanić, D., Epler, I., Adis, P., Biswas, S., Marinković, D., & Koprivica, S. (2024). Application of the DIBR II–rough MABAC decision-making model for ranking methods and techniques of lean organization systems management in the process of technical maintenance. Facta Universitatis, Series: Mechanical Engineering, 22(1), 101-123. https://doi.org/10.22190/FUME230614026B.

[63] Radovanović, M., Božanić, D., Tešić, D., Puška, A., Hezam, I., & Jana, C. (2023). Application of hybrid DIBR-FUCOM-LMAW-Bonferroni-Grey-EDAS model in multicriteria decision-making. Facta Universitatis, Series: Mechanical Engineering, 21(3), 387-403. https://doi.org/10.22190/FUME230824036R.

[64] Churchman, C. W., & Ackoff, R. L. (1954). An approximate measure of value. Journal of the Operations Research Society of America, 2(2), 172-187. https://doi.org/10.2307/21751.

[65] Hwang, C. L., & Yoon, K. (1981). Methods for multiple attribute decision making. Multiple attribute decision making: methods and applications a state-of-the-art survey, 58-191, Berlin, Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-48318-9.

[66] Gigović, L., Pamučar, D., Bajić, Z., & Milićević, M. (2016). The Combination of Expert Judgment and GIS-MAIRCA Analysis for the Selection of Sites for Ammunition Depots. Sustainability, 8(4), 372. https://doi.org/10.3390/su8040372.