Group Decision and Negotiation

, Volume 21, Issue 4, pp 519–530 | Cite as

Multicriteria Group Decision-Making Method Using Vector Similarity Measures For Trapezoidal Intuitionistic Fuzzy Numbers



Based on the extension of the Jaccard, Dice, and cosine similarity measures, three vector similarity measures between trapezoidal intuitionistic fuzzy numbers (TIFNs) are proposed in the vector space and are applied to the fuzzy multicriteria group decision-making problem, in which the criteria weights and the evaluated values in decision matrix are expressed by TIFNs. Through the weighted similarity measures between each alternative and the ideal alternative, the ranking order of all the alternatives can be determined and the best one(s) can be easily identified as well. A practical example of the developed approaches is given to select the investment alternatives. The decision results of different similarity measures demonstrate that the three similarity measures have better similarity identification. The illustrative example shows that the proposed methods are applicable.


Vector similarity measure Trapezoidal intuitionistic fuzzy number Multicriteria group decision making 


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  1. Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20: 87–96CrossRefGoogle Scholar
  2. Bellman R, Zadeh LA (1970) Decision making in a fuzzy environment. Manag Sci 17B(4): 141–164Google Scholar
  3. Chen CT (2000) Extensions of the TOPSIS for group decision-making under fuzzy environment. Fuzzy Sets Syst 114: 1–9CrossRefGoogle Scholar
  4. Chen SJ, Hwang CL (1992) Fuzzy multiple attribute decision making: methods and applications. Springer, BerlinCrossRefGoogle Scholar
  5. Dice LR (1945) Measures of the amount of ecologic association between species. Ecology 26: 297–302CrossRefGoogle Scholar
  6. Dubois D, Prade H (1983) Ranking fuzzy number in the setting of possibility theory. Information Sci 30: 183–224CrossRefGoogle Scholar
  7. Grzegrorzewski P (2003) The hamming distance between intuitionistic fuzzy sets. In: Proceedings of the 10th IFSA world congress. Istanbul, Turkey, pp. 35–38Google Scholar
  8. Herrera F, Herrera-Viedma E (2000) Linguistic decision analysis: steps for solving decision problems under linguistic information. Fuzzy Sets Syst 115: 67–82CrossRefGoogle Scholar
  9. He YY, Wang Q, Zhou DQ (2009) Extension of the expected value method for multiple attribute decision making with fuzzy data. Knowl Based Syst 22: 63–66CrossRefGoogle Scholar
  10. Hwang CL, Yoon K (1981) Multiple attribute decision making: methods and applications. Springer, BerlinCrossRefGoogle Scholar
  11. Jaccard P (1901) Distribution de la flore alpine dans le Bassin des Drouces et dans quelques regions voisines. Bull de la Société Vaudoise des Sciences Naturelles 37(140): 241–272Google Scholar
  12. Jahanshahloo GR, Hosseinzadeh Lotfi F, Izadikhah M (2006) Extension of the TOPSIS method for decision-making with fuzzy data. Appl Math Comput 181: 1544–1551CrossRefGoogle Scholar
  13. Kima MC, Choi KS (1999) A comparison of collocation-based similarity measures in query expansion. Inform Process Manag 35: 19–30CrossRefGoogle Scholar
  14. Nehi HM (2010) A new ranking method for intuitionistic fuzzy numbers. Int J Fuzzy Syst 12(1): 80–86Google Scholar
  15. Salton G, McGill MJ (1987) Introduction to modern information retrieval. McGraw-Hill, New YorkGoogle Scholar
  16. Wang YM, Parkan C (2005) Multiple attribute decision making based on fuzzy preference information on alternatives: ranking and weighting. Fuzzy Sets Syst 153: 331–346CrossRefGoogle Scholar
  17. Wu ZB, Chen YH (2007) The maximizing deviation method for group multiple attribute decision making under linguistic environment. Fuzzy Sets Syst 158: 1608–1617CrossRefGoogle Scholar
  18. Xu ZS (2004) Uncertain multiple attribute decision making: methods and applications. Tsinghua University Press, BeijingGoogle Scholar
  19. Xu ZS (2007) A method for multiple attribute decision making with incomplete weight information in linguistic setting. Knowl Based Syst 20: 719–725CrossRefGoogle Scholar
  20. Xu ZS (2010) A deviation-based approach to intuitionistic fuzzy multiple attribute group decision making. Group Decis Negot 19: 57–76CrossRefGoogle Scholar
  21. Ye J (2009) Multicriteria fuzzy decision-making method based on the intuitionistic fuzzy cross entropy. In: Proceedings of international conference of intelligent human-machine systems and cybernetics vol. 1. Hangzhou, Zhejiang, pp. 59–61Google Scholar
  22. Ye J (2010) Fuzzy decision-making method based on the weighted correlation coefficient under intuitionistic fuzzy environment. Eur J Oper Res 205: 202–204CrossRefGoogle Scholar
  23. Zeng L (2006) Expected value method for fuzzy multiple attribute decision making. Tsinghua Sci Technol 11(1): 102–106CrossRefGoogle Scholar

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© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of Mechatronics EngineeringShaoxing College of Arts and SciencesShaoxingPeople’s Republic of China

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