Mathematical modeling of the strategy of the battle of Siffin

Document Type : Original Article


University of Imam Ali, Iran


Mathematics has been applied to all sciences; and religious and military sciences are no exception, and mathematics can be used highly to design different war operations and solve battlefield equations to gain relative or absolute superiority over the enemy. We can also see clearly the application of mathematics in the Game Theory of war in abundance. In this applied research, conducted in a library method, the challenges between the army of Amir al-Mu’minin, ʿAlī ibn Abī Ṭālib (as) and the army of Muʿāwiya ibn Abī Sufyān in the Battle of Siffin have been modeled using Game Theory and the strategies of each of these two fronts are compared.
Finally, in order to examine the war utility, we seek to find the strategic equilibrium point between them. So, we obtain and discuss the utility function for each party's set of strategies in the battle of Siffin.


Abu Mikhnaf Kufi, Lut ibn Yahya, 1417 AH. Waqaa al-Taf, Scholar and Editor: Muhammad Hadi Yousefi Gharavi, Third Edition, Islamic Publications Office, Qom.
Akramizadeh et al. 1398 H.S. Strategic Gam Theory with an Islamic Approach with Emphasis on the Early Islamic Battles. AJA Strategic Studies Center.
Azghandi, Seyyed Alireza. 1394 H.S. War and Peace (Reviewing the Contemporary Military and Strategic Issues), Eighth Edition, Qom.
Balādhurī, ʾAḥmad ibn Yaḥyā, 1996 A.D. Jamal min Ansab al-Ashraf, Inquiry: Soheil Zakar and Riyadh Zarkeli, Dār al-Fikr, Beirut.
Berman, E., Shapiro, J.N. and Felter, J.H. 2011 A.D. "Can Hearts and Minds Be Bought the Economics of Counterinsurgency in Iraq", Journal of Political Economy, Vol. 119No. 4, pp. 766-819.
Boros, P., Fehér, O., Lakner, Z., Niroomand, S., & Vizvári, B. (2016). Modeling supermarket re-layout from the owner’s perspective. Annals of Operations Research238(1-2), 27-40.
B. O'neill. nd. "Game Theory Models of Peace and War"
Ebadi Zadeh, Hojjatollah, 1379 H.S. Mathematical Modeling of Interactions and Strategies of the Islamic Republic of Iran and Saudi Arabia Using Game Theory, The Scientific-Research Journal of Strategic Knowledge of Interdisciplinary Studies. Higher National Defense University.
Ibn Abi al-Hadid, nd. Description of Nahj al-Balāghah, research by Muhammad Abu al-Fazl Ibrahim, Dār Īhyā al-Turāth al-'Arabī, Beirut.
Ibn Asākir, Ali ibn Hassan. 1421 AH. History of Damascus, Inquiry by Abi Abdullah Ali Ashur al-Junoubi, Beirut, Dār Īhyā al-Turāth al-'Arabī.
Ibn A'tham. 1411 A.H. Al-Futūḥ, Beirut, Dār al-Nadveh.
Ibn Athir, 'Izz al-Din Abu al-Hassan. 1408 AH. Al-Kāmil fī al-tārīkh, Beirut, Dār Īhyā al-Turāth al-'Arabī.
Ibn Miskawayh, Abū ʿAlī, 1379 H.S. Tajārib al-Umam, Research by Abu al-Ghasem Emami, Soroush, Second T, Tehran.
Ibn Muzāḥim, Nasr. 1403 A.H. The Battle of Siffin, Inquiry by Abdul Salam Mohammad Aaron, Second Edition, Qom, Manshurat Maktabah al-Mar’ashi al-Najafi.
Lezgi, Ali Naghi et al. 1398 H.S. Mathematical Modeling of Gossip Propagation with a Defensive Approach by Looking at Verses and Narratives, Scientific-Research Journal of Strategic Knowledge Interdisciplinary Studies, No. 34.
Mirzaei, N., Niroomand, S., & Zare, R. (2016). Application of statistical process control in service industry: A case study of the restaurant sector. Journal of Modelling in Management.
Mosallaeipour, S., Mahmoodirad, A., Niroomand, S., & Vizvari, B. (2018). Simultaneous selection of material and supplier under uncertainty in carton box industries: a fuzzy possibilistic multi-criteria approach. Soft computing22(9), 2891-2905.
Niroomand, S. (2018). A multi-objective based direct solution approach for linear programming with intuitionistic fuzzy parameters. Journal of Intelligent & Fuzzy Systems35(2), 1923-1934.
Niroomand, S., Bazyar, A., Alborzi, M., & Mahmoodirad, A. (2018). A hybrid approach for multi-criteria emergency center location problem considering existing emergency centers with interval type data: a case study. Journal of Ambient Intelligence and Humanized Computing9(6), 1999-2008.
Niroomand, S., Hadi-Vencheh, A., Mirzaei, N., & Molla-Alizadeh-Zavardehi, S. (2016). Hybrid greedy algorithms for fuzzy tardiness/earliness minimisation in a special single machine scheduling problem: case study and generalisation. International Journal of Computer Integrated Manufacturing29(8), 870-888.
Niroomand, S., Takács, S., & Vizvári, B. (2011). To lay out or not to lay out?. Annals of Operations Research191(1), 183-192.
Niroomand, S., & Vizvári, B. (2013). A mixed integer linear programming formulation of closed loop layout with exact distances. Journal of Industrial and Production Engineering30(3), 190-201.
Niroomand, S., & Vizvari, B. (2015). Exact mathematical formulations and metaheuristic algorithms for production cost minimization: a case study of the cable industry. International Transactions in Operational Research22(3), 519-544.
Roshandel, Jalil. 1373 H.S. Military Strategy, Journal of Law and Political Science Faculty, University of Tehran. No. 31.
Salehi, M., Maleki, H. R., & Niroomand, S. (2020). Solving a new cost-oriented assembly line balancing problem by classical and hybrid meta-heuristic algorithms. Neural Computing and Applications32(12), 8217-8243.
Sadūq, Muhammad. 1395 A.H. Kamal al-Din and Tamam al-Nimah, Researcher and Editor: Ali Akbar Ghaffari, Second Edition, Dar al-Kutub al-Islamiyah, Tehran.
Sanei, M., Mahmoodirad, A., & Niroomand, S. (2016). Two-stage supply chain network design problem with interval data. International Journal of e-Navigation and Maritime Economy5, 74-84.
Sharman, J.C. 2015 A.D. “War, selection, and micro-states: Economic and sociological perspectives on the international system”, European Journal of International Relations, Vol. 21 No. 1, pp. 194-214.
Taassori, M., Niroomand, S., Uysal, S., Vizvari, B., & Hadi-Vencheh, A. (2018). Optimization approaches for core mapping on networks on chip. IETE Journal of Research64(3), 394-405.
Taassori, M., Niroomand, S., Uysal, S., Hadi-Vencheh, A., & Vizvari, B. (2016). Fuzzy-based mapping algorithms to design networks-on-chip. Journal of Intelligent & Fuzzy Systems31(1), 27-43.
Taassori, M., Taassori, M., Niroomand, S., Vizvári, B., Uysal, S., & Hadi-Vencheh, A. (2015). OPAIC: An optimization technique to improve energy consumption and performance in application specific network on chips. Measurement74, 208-220.
Ṭabarī, Muḥammad ibn Jarīr, Tarikh al-Umam wa al-Muluk, 1967 A.D. Research: Muhammad Abu al-Fazl Ibrahim, Dār al-Turāth, Beirut.
Tavana, M., Santos-Arteaga, F. J., Mahmoodirad, A., Niroomand, S., & Sanei, M. (2018). Multi-stage supply chain network solution methods: hybrid metaheuristics and performance measurement. International Journal of Systems Science: Operations & Logistics5(4), 356-373.
Vukovic, S. 2014 A.D. “International mediation as a distinct form of conflict management”, International Journal of Conflict Management, Vol. 25 No. 1, pp. 61-80.