Group multiple attribute decision making using a modified TOPSIS method in the presence of interval data

Document Type : Research Article

Authors

1 Department of Mathematics, Mobarakeh Branch, Islamic Azad University, Isfahan, Iran.

2 Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan, Iran.

10.24200/sci.2022.56712.4869

Abstract

Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is a well-known technique in multiple criteria  decision making and has found several applications in recent years. However, as mentioned in literature TOPSIS has  several shortcomings. In this paper, we present an extension of TOPSIS method to determine the weight of Decision Makers (DMs) in Group Multiple Attribute Decision Making (GMADM) problems with interval information. Our method is based on the concept that the best alternative is closer to the Positive Ideal Solution (PIS) and far away from the
Negative Ideal Solution (NIS), simultaneously. The contribution of the proposed method is that while it overcomes the shortcomings of the TOPSIS method it can be used to weight the decision making team and ranking the alternatives, as well. The method is illustrated through three examples.

Keywords

Main Subjects

References

References:
1. Arman, H. and Hadi-Vencheh, A. "The revised extent analysis method", Concurrency and Computation: Practice and Experience, 33(17), e6319 (2021). https://doi.org/10.1002/cpe.6319.
2. Gogate, N.G., Kalbar, P.P., and Raval P.M. "Assessment of stormwater management options in urban contexts using multiple attribute decision-making", Journal of Cleaner Production, 142, pp. 2046-2059 (2017). https://doi.org/10.1016/j.jclepro.2016.11.079.
3. Wang, Y.M., Liu, J., and Elhag, T.M.S. "An integrated AHP-DEA methodology for bridge risk assessment", Computers and Industrial Engineering, 54(3), pp. 513-525 (2008). https://doi.org/10.1016/j.cie.2007.09.002.
4. Chen, S.J. and Hwang, C.L., Fuzzy Multiple Attribute Decision Making: Methods and Applications, Springer- Verlag, NewYork (1992). https://doi.org/10.1007/978-3-642-46768-4.
5. Yousefi, A. and Hadi-Vencheh, A. "An integrated group decision making model and its evaluation by DEA for automobile industry", Expert Systems with Applications, 37, pp. 8543-8556 (2010). https://doi.org/10.1016/j.eswa.2010.05.021.
6. Georgiadis, D.R., Mazzuchi, T.A., and Sarkani, S. "Using multi criteria decision making in analysis of alternatives for selection of enabling technology", Systems Engineering, 16(3), pp. 287-303 (2013). https://doi.org/10.1002/sys.21233.
7. Golp^ra, H. "A novel Multiple Attribute Decision Making approach based on interval data using U2PMiner algorithm", Data and Knowledge Engineering, 115, pp. 116-128 (2018). https://doi.org/10.1016/j.datak.2018.03.001.
8. Karatas, M. "Multiattribute decision making using multiperiod probabilistic weighted fuzzy axiomatic design", Systems Engineering, 20(4), pp. 318-334 (2017). https://doi.org/10.1002/sys.21397.
9. Kumar Sen, D. "Analysis of decision support systems of industrial relevance: Application potential of fuzzy and grey set theories", Ph.D Dissertation, National Institute of Technology Rourkela, India (2017). Available at ethesis.nitrkl.ac.in.
10. Siddiqi, A., Ereiqat, F., and Anadon, L.D. "Formulating expectations for future water availability through infrastructure development decisions in arid regions", Systems Engineering, 19(2), pp. 101-110 (2016). https://doi.org/10.1002/sys.21337.
11. Wang, P., Zhu, Z., and Wang, Y. "A novel hybrid MCDM model combining the SAW, TOPSIS and GRA methods based on experimental design", Information Science, 345, pp. 27-45 (2016). https://doi.org/10.1016/j.ins.2016.01.076.
12. Wang, P., Meng, P., Zhai, J., et al. "A hybrid method experiment design and Grey Relational Analysis methods for multiple criteria decision making problems", Knowledge-Based Systems, 53, pp. 100-107 (2013). https://doi.org/10.1016/j.knosys.2013.08.025.
13. Hwang, C.L. and Yoon, K., Multiple Attribute Decision Making Methods and Applications, Springer-Verlag, Berlin (1981). https://doi.org/10.1007/978-3-642-48318-9.
14. Abootalebi, S., Hadi-Vencheh, A., and Jamshidi, A. "Ranking the alternatives with a modified TOPSIS method in multiple attribute decision making problems", IEEE Transactions on Engineering Management, 69(5), pp. 1800-1805 (2019). doi://10.1109/TEM.2019.2933593.
15. Jahanshahloo, G.R., Hosseinzadeh Lotfi, F., and Davoodi, A.R. "Extension of TOPSIS for decisionmaking problems with interval data: Interval efficiency", Mathematical and Computer Modelling, 49, pp. 1137-1142 (2009). https://doi.org/10.1016/j.mcm.2008.07.009.
16. Dymova, L., Sevastjanov, P., and Tikhonenko, A. "A direct interval extension of TOPSIS method", Expert Systems with Applications, 40, pp. 4841-4847 (2013). http://dx.doi.org/10.1016/j.eswa.2013.02.022.
17. Sa arzadeh, S., Jamshidi, A., and Hadi-Vencheh, A. "Relative agreement method for multiple criteria decision making problems with interval numbers", Scientia Iranica, 30(3), pp. 1169-1179 (2021). doi://10.24200/SCI.2021.54526.3794.
18. Sadabadi, S.A., Hadi-Vencheh, A., Jamshidi, A., et al. "A linear programming technique to solve fuzzy multiple criteria decision making problems with an application", RAIRO-Operations Research, 55(1), pp. 83-97 (2021). https://doi.org/10.1051/ro/2020116.
19. Chatterjee, K. and Kar, S. "Multi-criteria analysis of supply chain risk management using interval valued fuzzy TOPSIS", OPSEARCH, 53(3), pp. 474-499 (2016). https://doi.org/10.1007/s12597-015-0241-6.
20. Sadabadi, S.A., Hadi-Vencheh, A., Jamshidi, A., et al. "An improved fuzzy TOPSIS method with a new ranking index", International Journal of Information Technology and Decision Making, 21(2), pp. 615-641 (2021). https://doi.org/10.1142/S0219622021500620.
21. Lianga, D. and Xu, Z. "The new extension of TOPSIS method for multiple criteria decision making with hesitant pythagorean fuzzy sets", Applied Soft Computing, 60, pp. 167-179 (2017). https://doi.org/10.1016/j.asoc.2017.06.034.
22. Mahdavi, I., Heidarzade, A., Sadeghpour-Gildeh, B., et al. "A general fuzzy TOPSIS model in multiple criteria decision making", The International Journal of Advanced Manufacturing Technology, 45, pp. 406- 420 (2009). https://doi.org/10.1007/s00170-009-1971-5.
23. Shih, H.-S, Shyur, H.-J, and Stanley, L.E. "An extension of TOPSIS for group decision making", Mathematical and Computer Modelling, 45, pp. 801-813 (2007). https://doi.org/10.1016/j.mcm.2006.03.023.
24. Anisseh, M., Piri, F., Shahraki, M.R., et al. "Fuzzy extension of TOPSIS model for group decision making under multiple criteria", Artificial Intelligence Review, 38(4), pp. 325-338 (2012). https://doi.org/10.1007/s10462-011-9258-2.
25. Ataei, Y., Mahmoudi, I., Feylizadeh, M.R., et al. "Ordinal Priority Approach (OPA) in multiple attribute decision-making", Applied Soft Computing Journal, 86, Article no. 105893 (2020). https://doi.org/10.1016/j.asoc.2019.105893.
26. Yue, Z. "A method for group decision-making based on determining weights of decision makers using TOPSIS", Applied Mathematical Modelling, 35, pp. 1926- 1936 (2011). https://doi.org/10.1016/j.apm.2010.11.001.
27. Yue, Z. "An extended TOPSIS for determining weights of decision makers with interval numbers", Knowledge- Based Systems, 24, pp.146-153 (2011). https://doi.org/10.1016/j.knosys.2010.07.014.
28. Yue, Z. "Extension of TOPSIS to determine weight of decision maker for group decision making problems with uncertain information", Expert Systems with Applications, 39, pp. 6343-6350 (2012). https://doi.org/10.1016/j.eswa.2011.12.016.
29. Yue, Z. "Group decision making with multi-attribute interval data", Information Fusion, 14, pp. 551-561 (2013). https://doi.org/10.1016/j.inffus.2013.01.003.
30. Liu, S., Chan Felix, T.S., and Ran, W. "Multi attribute group decision-making with multigranularity linguistic assessment information: An improved approach based on deviation and TOPSIS", Applied Mathematical Modelling, 37, pp. 10129-10140 (2013). https://doi.org/10.1016/j.apm.2013.05.051.
31. Yang, Q., Du, P., Wang, Y., et al. "Developing a rough set based approach for group decision making based on determining weights of decision makers with interval numbers", Operational Research, 18(3), pp. 757-779 (2018). https://doi.org/10.1007/s12351-017-0344-3.
32. Kuo, T., "A modified TOPSIS with a different ranking index", European Journal of Operational Research, 260, pp. 152-160 (2017). https://doi.org/10.1016/j.ejor.2016.11.052.
33. Dwivedi, G, Srivastava, R.K., and Srivastava S.K. "A generalised fuzzy TOPSIS with improved closeness coefficient", Expert Systems With Applications, 96, pp. 185-195 (2018). https://doi.org/10.1016/j.eswa.2017.11.051.
34. Opricovic, S. and Tzeng, G.-H. "Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS", European Journal of Operational Research, 156, pp. 445-455 (2004). https://doi.org/10.1016/S0377-2217(03)00020-1.
35. Lai, Y.J, Liu, T.Y, and Hwang, C.L. "TOPSIS for MODM", European Journal of Operational Research, 76(3), pp. 486-500 (1994). https://doi.org/10.1016/0377-2217(94)90282-8.
36. Moore, R.E., Methods and Applications of interval analysis, SIAM Philadelfia, Pens (1979). https://doi.org/10.1137/1.9781611970906.
37. Ye, F. and Li, Y.N. "Group multi-attribute decision model to partner selection in the formation of virtual enterprise under incomplete information", Expert Systems with Applications, 36, pp. 350-9357 (2009). https://doi.org/10.1016/j.eswa.2009.01.015.
38. Mirzaei, N. and Testik, O.M. "Ideal location selection for new stone crusher machine and landfill using FAHP and TOPSIS method: a case study in a copper mine", Duzce Universitesi Bilim ve Teknoloji Dergisi, 9(5), pp. 1592-1609 (2021). https://doi.org/10.1016/j.eswa.2009.01.015.
Scientia Iranica
Volume 32, Issue 8
Transactions on Industrial Engineering (E)
March and April 2025 Article ID:4869

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History

  • Receive Date: 01 September 2020
  • Revise Date: 04 February 2022
  • Accept Date: 10 May 2022

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