Extension of VIKOR Method for MCDM Under Bipolar Fuzzy Set

Main Article Content

Bashayer Alsolame, Noura Omair Alshehri


In this paper, we extend the VIKOR method (Serbian name: VlseKriterijumska Optimizacija I Kompromisno Resenje, means multi-criteria optimization and compromise solution) to solve multi-criteria decision making (MCDM) with bipolar fuzzy environment. Firstly, the bipolar fuzzy set concept is described. Then, proposed the VIKOR strategy in bipolar set environment to handle MCDM problems. Finally, two numerical examples illustrate an application of BF-VIKOR method, and analysis the results of different values of the decision making weights of criteria on ranking order of the alternatives.

Article Details


  1. L. Zadeh, Fuzzy Sets, Information and Control. 8(3),(1965), 338-353.
  2. L. Zadeh, The concept of a linguistic variable and its application to approximate reasoning, Inform. Sci. 8 (3) (1975), 199-249.
  3. R. E. Bellman, L. A. Zadeh, Decision making in a fuzzy environment, Manage. Sci. 17 (4) (1970), 141-164.
  4. S. Opricovic, G.H. Tzeng, Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS, Eur. J. Oper. Res. 156 (2) (2004), 445-455.
  5. S. Opricovic, G.H. Tzeng, Extended VIKOR method in comparison with outranking methods, Eur. J. Oper. Res. 178 (2) (2004), 514-529.
  6. S. Opricovic, G.H. Tzeng, Multi-criteria planning of post-earthquake sustainable reconstruction, Comput.-Aided Civil Infr. Eng. 17 (3) (2002), 211-220.
  7. S. Opricovic, A fuzzy compromise solution for multicriteria problems, Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 15 (3) (2007), 363-380.
  8. T.C. Wang, T.H. Chang, Fuzzy VIKOR as a resolution for multi-criteria group decision-making, In The 11th International Conference on Industrial Engineering and Engineering Management. 2005, 352-356.
  9. A. Shemshadi, H. Shirazi, M. Toreihi, M.J. Tarokh, A fuzzy VIKOR method for supplier selection based on entropy measure for objective weighting. Expert Syst. Appl. 38 (10) (2011), 12160-12167.
  10. H.-C. Liu, L. Liu, J. Wu, Material selection using an interval 2-tuple linguistic VIKOR method considering subjective and objective weights, Mater. Des. (1980-2015). 52 (2013), 158-167.
  11. M.S. Kuo, G.S. Liang, A soft computing method of performance evaluation with MCDM based on interval-valued fuzzy numbers, Appl. Soft Comput. 12 (1) (2012), 476-485.
  12. A. Sanayei, S. F. Mousavi, A. Yazdankhah, Group decision making process for supplier selection with VIKOR under fuzzy environment, Expert Syst. Appl. 37 (1) (2010), 24-30.
  13. N. Yalcin, A. Bayrakdaroglu, C. Kahraman, Application of fuzzy multi-criteria decision making methods for financial performance evaluation of Turkish manufacturing industries, Expert Syst. Appl. 39 (1) (2012), 350-364.
  14. X. Y. Zhao, S. Tang, S. L. Yang, K.D Huang, Extended VIKOR method based on cross-entropy for interval-valued intuitionistic fuzzy multiple criteria group decision making, J. Intell. Fuzzy Syst. 25 (4) (2013), 1053-1066.
  15. K. Devi, Extension of VIKOR method in intuitionistic fuzzy environment for robot selection, Expert Syst. Appl. 38 (11) (2011), 14163-14168.
  16. N. Zhang, G.W Wei, Extension of VIKOR method for decision making problem based on hesitant fuzzy set, Appl. Math. Model. 37 (7) (2013), 4938-4947.
  17. W. R. Zhang, Yin-Yang bipolar fuzzy sets, In 1998 IEEE International Conference on Fuzzy Systems Proceedings. 1998, 835-840.
  18. P.L. Yu, A class of solutions for group decision problems. Manage. Sci. 19 (8) (1973), 936-946.
  19. M. Zeleny, Multiple Criteria Decision Making, McGraw-Hill, New York, 1982.