Document Type : Article

**Authors**

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

**Abstract**

So far, many ways have been provided to solve multiple criteria decision making problems with interval numbers. Most of these methods rank the alternatives according to two criteria, that is, being close to the positive ideal solution and far away from the negative ideal solution. In this paper, a method is presented for solving multiple criteria decision making problems with interval numbers, such that being close to positive ideal solution and being away from negative ideal solution have the same effect in alternatives ranking. In the proposed method, the first positive ideal solution and negative ideal solution are determined as interval numbers and distance of each alternative from positive ideal solution and negative ideal solution is calculated by extension of Euclidean distance. Then, a compromise index is defined to rank the alternatives. Three numerical examples are given to compare the proposed method with other methods presented in the literature.

**Keywords**

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15. Jahanshahloo, G.R., Lotfi, F.H., and Davoodi, A.R. "Extension of TOPSIS for decision-making problems with interval data: Interval efficiency", Mathematical and Computer Modelling, 49(5-6), pp. 1137-1142 (2009).

16. Sayadi, M.K., Heydari, M., and Shahanaghi, K. "Extension of VIKOR method for decision making problem with interval numbers", Applied Mathematical Modelling, 33(5), pp. 2257-2262 (2009).

17. Dymova, L., Sevastjanov, P., and Tikhonenko, A. "A direct interval extension of TOPSIS method", Expert Systems with Applications, 40(12), pp. 4841- 4847 (2013).

18. Hafezalkotob, A., Hafezalkotob, A., and Sayadi, M.K. "Extension of MULTIMOORA method with interval numbers: an application in materials selection", Applied Mathematical Modelling, 40(2), pp. 1372-1386 (2016).

19. Jahan, A. and Edwards, K.L. "VIKOR method for material selection problems with interval numbers and target-based criteria", Materials & Design, 47, pp. 759-765 (2013).

20. Xu, Z. "On method for uncertain multiple attribute decision making problems with uncertain multiplicative preference information on alternatives", Fuzzy Optimization and Decision Making, 4(2), pp. 131-139 (2005).

21. Xu, Z. "Dependent uncertain ordered weighted aggregation operators" Information Fusion, 9(2), pp. 310- 316 (2008).

22. Saffarzadeh, S., Hadi-Vencheh, A., and Jamshidi, A. "Weight determination and ranking priority in interval group MCDM", Scientia Iranica, 27(6), pp. 3242-3252 (2020).

2. Hwang, C.L. and Yoon, K., Multiple Attribute Decision Making: Methods and Applications, Springer, New York (1981).

3. Zavadskas, E.K., Kaklauskas, A., and Sarka, V. "The new method of multi-criteria complex proportional assessment of projects", Technological and Economic Development of Economy, 1(3), pp. 131-139 (1994).

4. Zavadskas, E.K., Antucheviciene, J., Turskis, Z., et al. "Hybrid multiple-criteria decision-making methods: A review of applications in engineering", Scientia Iranica, 23(1), pp. 1-20 (2016).

5. Govindan, K. and Jepsen, M.B. "ELECTRE: A comprehensive literature review on methodologies and applications", European Journal of Operational Research, 250(1), pp. 1-29 (2016).

6. Carneiro, J., Conceicao, L., Martinho, D., et al. "Including cognitive aspects in multiple criteria decision analysis", Annals of Operations Research, 265(2), pp. 269-291 (2018).

7. MacCrimmon, K.R. "Decision making among multiple-attribute alternatives: a survey and consolidated approach", Rand Corp Santa Monica Ca (1968).

8. Opricovic, S. "Multicriteria optimization of civil engineering systems", Faculty of Civil Engineering, Belgrade, 2(1), pp. 5-21 (1998).

9. Abdollahi, A. and Pour-Moallem, N. "Dynamic negawatt demand response resource modeling and prioritizing in power markets", Scientia Iranica, 27(3), pp. 1361-1372 (2020). DOI: 10.24200/sci.2017.4406.

10. Kirubakaran, B. and Ilangkumaran, M. "Selection of optimum maintenance strategy based on FAHP integrated with GRA-TOPSIS", Annals of Operations Research, 245(1-2), pp. 285-313 (2016).

11. Singh, R.K., Gunasekaran, A., and Kumar, P. "Third party logistics (3PL) selection for cold chain management: a fuzzy AHP and fuzzy TOPSIS approach", Annals of Operations Research, 267, pp. 531-553 (2018).

12. Mahmoudi, A., Sadi-Nezhad, S., and Makui, A. "An extended fuzzy VIKOR for group decision-making based on fuzzy distance to supplier selection", Scientia Iranica, Transaction E, Industrial Engineering, 23(4), p. 1879 (2016).

13. Hu, J., Chen, P., and Chen, X. "Intuitionistic random multi-criteria decision-making approach based on prospect theory with multiple reference intervals", Scientia Iranica, Transaction E, Industrial Engineering, 21(6), p. 2347 (2014).

14. Jahanshahloo, G.R., Lotfi, F.H., and Izadikhah, M. "An algorithmic method to extend TOPSIS for decision-making problems with interval data", Applied Mathematics and Computation, 175(2), pp. 1375-1384 (2006).

15. Jahanshahloo, G.R., Lotfi, F.H., and Davoodi, A.R. "Extension of TOPSIS for decision-making problems with interval data: Interval efficiency", Mathematical and Computer Modelling, 49(5-6), pp. 1137-1142 (2009).

16. Sayadi, M.K., Heydari, M., and Shahanaghi, K. "Extension of VIKOR method for decision making problem with interval numbers", Applied Mathematical Modelling, 33(5), pp. 2257-2262 (2009).

17. Dymova, L., Sevastjanov, P., and Tikhonenko, A. "A direct interval extension of TOPSIS method", Expert Systems with Applications, 40(12), pp. 4841- 4847 (2013).

18. Hafezalkotob, A., Hafezalkotob, A., and Sayadi, M.K. "Extension of MULTIMOORA method with interval numbers: an application in materials selection", Applied Mathematical Modelling, 40(2), pp. 1372-1386 (2016).

19. Jahan, A. and Edwards, K.L. "VIKOR method for material selection problems with interval numbers and target-based criteria", Materials & Design, 47, pp. 759-765 (2013).

20. Xu, Z. "On method for uncertain multiple attribute decision making problems with uncertain multiplicative preference information on alternatives", Fuzzy Optimization and Decision Making, 4(2), pp. 131-139 (2005).

21. Xu, Z. "Dependent uncertain ordered weighted aggregation operators" Information Fusion, 9(2), pp. 310- 316 (2008).

22. Saffarzadeh, S., Hadi-Vencheh, A., and Jamshidi, A. "Weight determination and ranking priority in interval group MCDM", Scientia Iranica, 27(6), pp. 3242-3252 (2020).

Transactions on Industrial Engineering (E)

May and June 2023Pages 1169-1179