Quarterly Publication

Document Type : Original Article


Department of Industrial Engineering, Parand Branch, Islamic Azad University, Parand, Iran.


There are numerous and various methods for solving the Multi-Attribute Decision-Making (MADM) problems in the literature, such as Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), Elimination and Choice Expressing Reality (ELECTRE), Analytic Hierarchy Process (AHP), etc. We have explored Support Vector Machine (SVM) as an efficient method for solving MADM problems. The SVM technique was proposed for classifying data at first. At the same time, in the current research, this popular method will be used to sort the preference alternatives in a MADM problem with interval data. The accuracy of the proposed technique will be compared with a popular extended method for interval data, say interval TOPSIS. Numerical experiments showed that admissible results can be obtained by the new method.


[1]   Jahanshahloo, G. R., Lotfi, F. H., & Davoodi, A. R. (2009). Extension of TOPSIS for decision-making problems with interval data: Interval efficiency. Mathematical and computer modelling, 49(5–6), 1137–1142.
[2]   Rasinojehdehi, R., & Valami, H. B. (2023). A comprehensive neutrosophic model for evaluating the efficiency of airlines based on SBM model of network DEA. Decision making: applications in management and engineering, 6(2), 880–906.
[3]   Nozari, H., Najafi, E., Fallah, M., & Hosseinzadeh Lotfi, F. (2019). Quantitative analysis of key performance indicators of green supply chain in FMCG industries using non-linear fuzzy method. Mathematics, 7(11), 1020. https://doi.org/10.3390/math7111020
[4]   Najafi, S. E., Amiri, M., & Abdolah Zadeh, V. (2015). Ranking practicable technologies within the science and technology corridor of Isfahan, using MCDM techniques. Journal of applied research on industrial engineering, 2(3), 139–153.
[5]   Rasi Nojehdehi, R., Bagherzadeh Valami, H., & Najafi, S. E. (2023). Classifications of linking activities based on their inefficiencies in Network DEA. International journal of research in industrial engineering, 12(2), 165–176.
[6]   Seiti, H., Hafezalkotob, A., Najafi, S. E., & Khalaj, M. (2019). Developing a novel risk-based MCDM approach based on D numbers and fuzzy information axiom and its applications in preventive maintenance planning. Applied soft computing, 82, 105559. https://doi.org/10.1016/j.asoc.2019.105559
[7]   Zeleny, M. (1982). Multiple criteria decision making. McGraw Hill.
[8]   Chen, S. J., & Hwang, C. L. (1992). Fuzzy multiple attribute decision making methods. In Fuzzy multiple attribute decision making: methods and applications (pp. 289–486). Springer.
[9]   Chen, T.-Y., & Tsao, C.-Y. (2008). The interval-valued fuzzy TOPSIS method and experimental analysis. Fuzzy sets and systems, 159(11), 1410–1428.
[10] Wang, Y. M., & Elhag, T. M. S. (2006). Fuzzy TOPSIS method based on alpha level sets with an application to bridge risk assessment. Expert systems with applications, 31(2), 309–319.
[11] Sayadi, M. K., Heydari, M., & Shahanaghi, K. (2009). Extension of VIKOR method for decision making problem with interval numbers. Applied mathematical modelling, 33(5), 2257–2262.
[12] Xue-jun, T., & Jia, C. (2012). A dynamic interval decision-making method based on GRA. Physics procedia, 24, 2017–2025.
[13] Khefacha, I., & Belkacem, L. (2015). Modeling entrepreneurial decision-making process using concepts from fuzzy set theory. Journal of global entrepreneurship research, 5, 1–21.
[14]    Hwang, C. L., Yoon, K., 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, 186, 58–191. https://link.springer.com/chapter/10.1007/978-3-642-48318-9_3
[15]    Olson, D. L. (2004). Comparison of weights in TOPSIS models. Mathematical and computer modelling, 40(7–8), 721–727.
[16]    Lai, Y.-J., Liu, T.-Y., & Hwang, C.-L. (1994). Topsis for MODM. European journal of operational research, 76(3), 486–500.
[17]    Abo-Sinna, M. A., & Amer, A. H. (2005). Extensions of TOPSIS for multi-objective large-scale nonlinear programming problems. Applied mathematics and computation, 162(1), 243–256.
[18]    Kuo, M. S., Tzeng, G. H., & Huang, W. C. (2007). Group decision-making based on concepts of ideal and anti-ideal points in a fuzzy environment. Mathematical and computer modelling, 45(3–4), 324–339.
[19]    Shih, H.-S., Shyur, H.-J., & Lee, E. S. (2007). An extension of TOPSIS for group decision making. Mathematical and computer modelling, 45(7–8), 801–813.
[20]    Yue, Z. (2013). Group decision making with multi-attribute interval data. Information fusion, 14(4), 551–561.
[21]    Behzadian, M., Otaghsara, S. K., Yazdani, M., & Ignatius, J. (2012). A state-of the-art survey of TOPSIS applications. Expert systems with applications, 39(17), 13051–13069.
[22]    Salih, M. M., Zaidan, B. B., Zaidan, A. A., & Ahmed, M. A. (2019). Survey on fuzzy TOPSIS state-of-the-art between 2007 and 2017. Computers & operations research, 104, 207–227.
[23]    Sengupta, A., & Pal, T. K. (2000). On comparing interval numbers. European journal of operational research, 127(1), 28–43.
[24]    Delgado, M., Vila, M. A., & Voxman, W. (1998). A fuzziness measure for fuzzy numbers: Applications. Fuzzy sets and systems, 94(2), 205–216.
[25]    Cortes, C., & Vapnik, V. (1995). Support-vector networks. Machine learning, 20, 273–297.