Document Type : Research Paper


1 Young Researchers and Elite Club, Arak Branch, Islamic Azad University, Arak, Iran.

2 Department of Industrial Engineering, Islamic Azad University of Arak, Arak, Iran.


The VIKOR method was developed for Multi-Criteria Decision Making (MCDM). It determines the compromise ranking list and the compromise solution obtained with the initial weights. This method focuses on ranking and selecting from a set of alternatives in the presence of conflicting criteria. It introduces the multi-criteria ranking index based on the particular measure of ‘‘closeness” to the “Ideal” solution. The aim of this paper is to extend the VIKOR method for decision making problems with interval number. The extended VIKOR method’s ranking is obtained through comparison of interval numbers and for doing the comparisons between intervals. In the end, a numerical example illustrates and clarifies the main results developed in this paper.


Main Subjects

[1]        Yu, P. L. (1973). A class of solutions for group decision problems. Management science19(8), 936-946.
[2]        Zeleny, M. (Ed.). (2012). Multiple criteria decision making Kyoto 1975 (Vol. 123). Springer Science & Business Media.
[3]        Yu, P. L. (2013). Multiple-criteria decision making: concepts, techniques, and extensions (Vol. 30). Springer Science & Business Media.
[4]        Tzeng, G. H., & Huang, J. J. (2011). Multiple attribute decision making: methods and applications. CRC press.
[5]        triantaphyllou, E. (2000). multi-criteria decision making methods: a comparative study. kluwer academic publishers, dordrecht.
[6]        wang, h. f. (2000). Fuzzy multicriteria decision making—an overview. Journal of intelligent & Fuzzy Systems9(1, 2), 61-83.
[7]        Chen, S. J., & Hwang, C. L. (1991). Fuzzy multiple attribute decision making. Springer Verlag, Berlin.
[8]        Ribeiro, R. A. (1996). Fuzzy multiple attribute decision making: a review and new preference elicitation techniques. Fuzzy sets and systems78(2), 155-181.
[9]        Prékopa, A. (2013). Stochastic programming (Vol. 324). Springer Science & Business Media.
[10]    Sengupta, J. K. (1981). Optimal decision under uncertainty. Springer, New York.
[11]    Vajda, S. (1972). Probabilistic programming. Academic Press, New York.
[12]    Liu, X. (2004). On the methods of decision making under uncertainty with probability information. International journal of intelligent systems19(12), 1217-1238.
[13]    Moore, R. E. (1979). Method and application of interval analysis. SIAM, Philadelphia.
[14]    Jahanshahloo, G. R., Lotfi, F. H., & Izadikhah, M. (2006). An algorithmic method to extend TOPSIS for decision-making problems with interval data. Applied mathematics and computation175(2), 1375-1384.
[15]    Opricovic, S., & Tzeng, G. H. (2004). Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS. European journal of operational research156(2), 445-455.
[16]    Opricovic, S., & Tzeng, G. H. (2007). Extended VIKOR method in comparison with outranking methods. European journal of operational research178(2), 514-529.
[17]    Choobineh, F., & Behrens, A. (1993). Use of intervals and possibility distributions in economic analysis. Journal of the operational research society43(9), 907-918.
[18]    Sengupta, A., & Pal, T. K. (2006). Solving the shortest path problem with interval arcs. Fuzzy optimization and decision making5(1), 71-89.
[19]    Alefeld, G., & Herzberger, J. (2012). Introduction to interval computation. Academic press.
[20]    Kearfott, R. B., & Kreinovich, V. (Eds.). (2013). Applications of interval computations (Vol. 3). Springer Science & Business Media.
[21]    Shaocheng, T. (1994). Interval number and fuzzy number linear programmings. Fuzzy sets and systems66(3), 301-306.
[22]    Moore, R., & Lodwick, W. (2003). Interval analysis and fuzzy set theory. Fuzzy sets and systems135(1), 5-9.
[23]    Bhattacharyya, R. (2015). A grey theory based multiple attribute approach for R&D project portfolio selection. Fuzzy information and engineering7(2), 211-225.