ABSTRACT:
Interval numbers play a significant role in uncertain decision making process. However, interval numbers ranking have always been a challenging task in the field of decision making under uncertain conditions. Several solutions for the above problem are possible (i.e., the acceptability index, minimax regret approach, etc.), but theoretically there is no reason to be restricted to these approaches. Therefore, in this paper, we propose the distance to ideal interval numbers model to evaluates the non-negative interval numbers based on the distance between each interval number and the ideal interval numbers. So, interval numbers are ranked according to proximity to ideal interval numbers. Moreover, the comparative study of above approach with existing approach (particularly, the acceptability index) is also addressed. Results show the feasibility and effectiveness of each approach.
Cite this article:
Mohammad Azadfallah. An Alternative Interval Numbers Ranking Method based on Distance to the Ideal Interval Numbers. Asian Journal of Management. 2025;16(4):311-6. doi: 10.52711/2321-5763.2025.00047
Cite(Electronic):
Mohammad Azadfallah. An Alternative Interval Numbers Ranking Method based on Distance to the Ideal Interval Numbers. Asian Journal of Management. 2025;16(4):311-6. doi: 10.52711/2321-5763.2025.00047 Available on: https://ajmjournal.com/AbstractView.aspx?PID=2025-16-4-9
REFERENCES:
1. Amiri, M., Nosratian, N. E., Jamshidi, A., and Kazemi, A. Developing a new ELECTRE method with interval data in multi attribute decision making problems. Journal of Applied Sciences. 2008; 8(22): 4017-4028.
2. Amiri, M., Zandian, M., Vahdani, B., Yazdani, M., and Soltani, R. A hybrid MCDM model with interval weights and data for convention site selection. Journal of Applied Sciences. 2008; 8(15): 2678-2686.
3. Anand, A. Agarawal, M. and Aggrawal, D. Multiple Criteria Decision Making methods: Application for Managerial Discretion. 2022 Walter de Gruyter GmbH, Berlin/Boston. 2022.
4. Azadfallah, M. Supplier selection with interval SAW for a group of decision makers when a group cannot reach to consensus. Journal of Supply Chain Management System. 2017; 6(3): 25-34.
5. Azadfallah, M. A new MCDM approach for ranking of candidates in voting systems. Int. J. Society Systems Sciences. 2019; 11(2): 119-133.
6. Fan, Z. P. and Liu, Y. An approach to solve group decision making problems with ordinal interval numbers. Cybern B Cybern. 2010; 40(5): 1413-23.
7. Hadiono, K. A practical implementation of interval arithmetic in AHP. IJAHP. 2016; 8(2).
8. Hosseinzadeh, A. and Ghasemi, M. V. Solving fully interval linear programming problems using ranking interval numbers. International Journal Industrial Mathematics. 2021; 13(3): 1-12.
9. Jiang, J., Ren, M., and Wang, J. Interval number Multi Attribute Decision making method based on TOPSIS. Alexandria Engineering Journal. 2022; 61(7): 5059-5064.
10. Liu, J. S. The ranking of interval numbers. Chines Journal of Engineering Mathematics. 2001; 18(4): 103-109.
11. Li, D., Zeng, W., and Yin, Q. Novel ranking method of interval numbers based on the Boolean matrix. Soft Computing. 2018; 22: 4113-4122.
12. Nenad, M. and Zoran, A. Multi-Criteria Decision Making method comparative analysis of PROMETHEE and VIKOR. XVII International Scientific Conference on Industrial Systems (IS’17), Novi Sad, Serbia. 2017: 284-287.
13. Qu, Z., Wan, C., Yang, Z., and Lee, P. T. W. A discourse of Multi Criteria Decision making (MCDM) approaches, Ch.2 [pp.8], in: P. T. W. Lee, Z. Yang (eds.), Multi Criteria Decision making, in marine studies and logistics, Springer International Publishing AG 2018.
14. Romanenkov, Y. Criterion for ranking interval alternatives in a decision making task. I. J. Modern Education and Computer Science. 2024; 2: 72-82.
15. Roszkowska, E. Multi-Criteria Decision making models by applying the TOPSIS method to crisp and interval data. Multi-Criteria Decision making/University of Economics in Katowice. 2011; 6: 200-230.
16. Sayadi, M. K., Heydari, M. and Shahanaghi, K. Extension of VIKOR method for decision making problem with interval numbers. Applied Mathematical Modelling. 2009; 33: 2257-2262.
17. Sengupta, A. and Pal, T. K. Fuzzy preference ordering of interval numbers in decision problems. Springer-Verlag Berlin Heidelberg 2009.
18. Sengupta, A., Pal, T. K., and Chakraborty, D. Interpretation of inequality constraints involving interval coefficients and a solution to interval linear programming. Fuzzy Sets and Systems. 2001; 119: 129-138.
19. Sevastianov, P. Numerical methods for interval and fuzzy number comparison based on the probabilistic approach and Dempster-Shafer theory. Information Sciences. 2007; 177(21): 4645-4661.
20. Sitorus, F., Cilliers, J. J., and Parada, P. R. B. Multi-Criteria Decision Making for the choice problem in mining and mineral processing: applications and trends. Expert Systems with Applications. 2019; 121: 393-417.
21. Song, P., Liang, J., and Qian, Y. A two-grade approach to ranking interval data. Knowledge-Based Systems. 2012; 27: 234-244.
22. Triantaphyllou, E., Shu, B., Sanchez, S. N., and Ray, T. Multi-Criteria Decision making: An operations research approach. Encyclopedia of Electrical and Electronics Engineering, (J. G. Webster, Ed.), John Wiley and Sons, New York, NY. 1998; 15: 175-186.
23. Wang, W. J. Ranking and application of interval numbers based on partial connection numbers. Journal of Gansu Education College. 2008; 1: 48-50.
24. Yao, N., Ye, Y., Wang, Q., and Hu, N. Interval number ranking method considering multiple decision. Iranian Journal of Fuzzy Systems. 2020; 17(2): 115-127.
25. Yue, C. A novel approach to interval comparison and application to software quality evaluation. Journal of Experimental and Theoretical Artificial Intelligence. 2018; 30(5): 583-602.
26. Yue Z. Group decision making with Multi attribute interval data. Information Fusion. 2013; 14: 551-561.
27. Zakeri, S., Cheikhrouhou, N., Konstantas, D., and Barabadi, F. S. (2022). A grey approach for the computation of interactions between two groups of irrelevant variables of decision matrices. Ch. 10[pp. 193-222],
28. A. J. Kulkarni [Editor]: Multi Criteria Decision making; techniques, analysis and applications, Studies in Systems, Decision and Control 407, Springer Nature Singapore Ptd Ltd.
29. Zavadskas, E. K., Antucheviciene, J., Turskis, Z., Adeli, H. Hybrid Multi-Criteria Decision Making methods: A review of applications in engineering, Scientia Iranica. 2016; 23(1): 1-20.
30. Zhang, Y. and Xu, J. The ELECTRE method based on interval numbers and its application to the selection of leather manufacture alternatives. World Journal of Modelling and Simulation. 2006; 2(2): 119-128.