International Journal of Fuzzy Systems

, Volume 19, Issue 5, pp 1279–1289 | Cite as

Analyzing the Ranking Method for Fuzzy Numbers in Fuzzy Decision Making Based on the Magnitude Concepts

  • Vincent F. Yu
  • Luu Huu Van
  • Luu Quoc DatEmail author
  • Ha Thi Xuan Chi
  • Shuo-Yan Chou
  • Truong Thi Thuy Duong


Ranking fuzzy numbers is an important component in the decision-making process with the last few decades having seen a large number of ranking methods. Ezzati et al. (Expert Syst Appl 39:690–695, 2012) proposed a revised approach for ranking symmetric fuzzy numbers based on the magnitude concepts to overcome the shortcoming of Abbasbandy and Hajjari’s method. Despite its merits, some shortcomings associated with Ezzati et al.’s approach include: (1) it cannot consistently rank the fuzzy numbers and their images; (2) it cannot effectively rank symmetric fuzzy numbers; and (3) it cannot rank non-normal fuzzy numbers. This paper thus proposes a revised method to rank generalized and/or symmetric fuzzy numbers in parametric forms that can surmount these issues. In the proposed ranking method, a novel magnitude of fuzzy numbers is proposed. To differentiate the symmetric fuzzy numbers, the proposed ranking method takes into account the decision maker’s optimistic attitude of fuzzy numbers. We employ several comparative examples and an application to demonstrate the usages and advantages of the proposed ranking method. The results conclude that the proposed ranking method effectively resolves the issues with Ezzati et al.’s ranking method. Moreover, the proposed ranking method can differentiate different types of fuzzy numbers.


Generalized fuzzy numbers Magnitude concept Fuzzy ranking method Fuzzy decision making 



This research was partially supported by the Ministry of Science and Technology of the Republic of China (Taiwan) under grant MOST 103-2221-E-011-062-MY3 and the Vietnam Institute for Advanced Study in Mathematics (VIASM). These supports are gratefully acknowledged. This work was completed during the stay of the third author at the Vietnam Institute for Advanced Study in Mathematics (VIASM)


  1. 1.
    Jain, R.: Decision-making in the presence of fuzzy variables. IEEE Trans. Syst. Man Cybern. 6, 698–703 (1976)zbMATHGoogle Scholar
  2. 2.
    Chai, K.C., Tay, K.M., Lim, C.P.: A new method to rank fuzzy numbers using Dempster–Shafer theory with fuzzy targets. Inf. Sci. 346–347, 302–317 (2016)CrossRefGoogle Scholar
  3. 3.
    Das, S., Guha, D.: A centroid-based ranking method of trapezoidal intuitionistic fuzzy numbers and its application to MCDM problems. Fuzzy Inf. Eng. 8, 41–74 (2016)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Wang, Y.J.: Ranking triangle and trapezoidal fuzzy numbers based on the relative preference relation. Appl. Math. Model. 39, 586–599 (2015)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Yu, V.F., Dat, L.Q.: An improved ranking method for fuzzy numbers with integral values. Appl. Soft Comput. 14, 603–608 (2014)CrossRefGoogle Scholar
  6. 6.
    Chu, T.C., Charnsethikul, P.: Ordering alternatives under fuzzy multiple criteria decision making via a fuzzy number dominance based ranking approach. Int. J. Fuzzy Syst. 15, 263–273 (2013)MathSciNetGoogle Scholar
  7. 7.
    Dat, L.Q., Yu, V.F., Chou, S.Y.: An improved ranking method for fuzzy numbers based on the centroid-index. Int. J. Fuzzy Syst. 14, 413–419 (2012)MathSciNetGoogle Scholar
  8. 8.
    Chen, S.H.: Ranking fuzzy numbers with maximizing set and minimizing set. Fuzzy Sets Syst. 17, 113–129 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Liou, T.S., Wang, M.J.: Ranking fuzzy numbers with integral value. Fuzzy Sets Syst. 50, 247–255 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Cheng, C.H.: A new approach for ranking fuzzy numbers by distance method. Fuzzy Sets Syst. 95, 307–317 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Chu, T.C., Tsao, C.T.: Ranking fuzzy numbers with an area between the centroid point and original point. Comput. Math Appl. 43, 111–117 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Asady, B., Zendehnam, A.: Ranking fuzzy numbers by distance minimization. Appl. Math. Model. 3(11), 2589–2598 (2007)CrossRefzbMATHGoogle Scholar
  13. 13.
    Abbasbandy, S., Hajjari, T.: A new approach for ranking of trapezoidal fuzzy numbers. Comput. Math Appl. 57(3), 413–419 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Ezzati, R., Allahviranloo, T., Khezerloo, S., Khezerloo, M.: An approach for ranking of fuzzy numbers. Expert Syst. Appl. 39, 690–695 (2012)CrossRefzbMATHGoogle Scholar
  15. 15.
    Goetsche, R., Voxman, W.: Elementary calculus. Fuzzy Sets Syst. 18, 31–43 (1986)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Ma, M., Friedman, M., Kandel, A.: A new fuzzy arithmetic. Fuzzy Sets Syst. 108, 83–90 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Zimmermann, H.J.: Fuzzy Set Theory and its Applications. Kluwer Academic Press, Dordrecht (1991)CrossRefzbMATHGoogle Scholar
  18. 18.
    Chou, S.Y., Dat, L.Q., Vincent, F.Y.: A revised method for ranking fuzzy numbers using maximizing set and minimizing set. Comput. Ind. Eng. 61, 1342–1348 (2011)CrossRefGoogle Scholar
  19. 19.
    Wang, X., Kerre, E.E.: Reasonable properties for the ordering of fuzzy quantities I. Fuzzy Sets Syst. 118, 375–385 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Wang, Y.J., Lee, H.S.: The revised method of ranking fuzzy numbers with an area between the centroid and original points. Comput. Math Appl. 55(9), 2033–2042 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Abbasbandy, S., Asady, B.: Ranking of fuzzy numbers by sign distance. Inform. Sci. 176, 2405–2416 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Asady, B.: The revised method of ranking LR fuzzy number based on deviation degree. Expert Syst. Appl. 37(7), 5056–5060 (2010)CrossRefGoogle Scholar
  23. 23.
    Wang, Y.M., Luo, Y.: Area ranking of fuzzy numbers based on positive and negative ideal points. Comput. Math Appl. 58, 1769–1779 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Wang, Z.X., Liu, Y.J., Fan, Z.P., Feng, B.: Ranking L–R fuzzy number based on deviation degree. Inf. Sci. 179(13), 2070–2077 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Centra, J.A.: How Universities Evaluate Faculty Performance: A Survey of Department Heads. Graduate Record Examinations Program Educational Testing Service, Princeton, NJ 08540, (1977)Google Scholar
  26. 26.
    Wood, F.: Factors influencing research performance of university academic staff. High. Educ. 19, 81–100 (1990)CrossRefGoogle Scholar
  27. 27.
    Dursun, M., Karsak, E.E.: A fuzzy MCDM approach for personnel selection. Expert Syst. Appl. 37, 4324–4330 (2010)CrossRefGoogle Scholar
  28. 28.
    Chu, T.C., Lin, Y.C.: A fuzzy TOPSIS method for robot selection. Int. J. Adv. Manuf. Technol. 21, 284–290 (2003)CrossRefGoogle Scholar

Copyright information

© Taiwan Fuzzy Systems Association and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Vincent F. Yu
    • 1
  • Luu Huu Van
    • 1
  • Luu Quoc Dat
    • 2
    Email author
  • Ha Thi Xuan Chi
    • 3
  • Shuo-Yan Chou
    • 1
  • Truong Thi Thuy Duong
    • 4
  1. 1.Department of Industrial ManagementNational Taiwan University of Science and TechnologyTaipeiTaiwan
  2. 2.University of Economics and BusinessVietnam National UniversityHanoiVietnam
  3. 3.International UniversityVietnam National UniversityHo Chi MinhVietnam
  4. 4.Banking AcademyHanoiVietnam

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