Skip to main content
Log in

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

International Journal of Fuzzy Systems Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

References

  1. Jain, R.: Decision-making in the presence of fuzzy variables. IEEE Trans. Syst. Man Cybern. 6, 698–703 (1976)

    MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  4. Wang, Y.J.: Ranking triangle and trapezoidal fuzzy numbers based on the relative preference relation. Appl. Math. Model. 39, 586–599 (2015)

    Article  MathSciNet  Google Scholar 

  5. Yu, V.F., Dat, L.Q.: An improved ranking method for fuzzy numbers with integral values. Appl. Soft Comput. 14, 603–608 (2014)

    Article  Google Scholar 

  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)

    MathSciNet  Google Scholar 

  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)

    MathSciNet  Google Scholar 

  8. Chen, S.H.: Ranking fuzzy numbers with maximizing set and minimizing set. Fuzzy Sets Syst. 17, 113–129 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  9. Liou, T.S., Wang, M.J.: Ranking fuzzy numbers with integral value. Fuzzy Sets Syst. 50, 247–255 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  10. Cheng, C.H.: A new approach for ranking fuzzy numbers by distance method. Fuzzy Sets Syst. 95, 307–317 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  12. Asady, B., Zendehnam, A.: Ranking fuzzy numbers by distance minimization. Appl. Math. Model. 3(11), 2589–2598 (2007)

    Article  MATH  Google Scholar 

  13. Abbasbandy, S., Hajjari, T.: A new approach for ranking of trapezoidal fuzzy numbers. Comput. Math Appl. 57(3), 413–419 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  14. Ezzati, R., Allahviranloo, T., Khezerloo, S., Khezerloo, M.: An approach for ranking of fuzzy numbers. Expert Syst. Appl. 39, 690–695 (2012)

    Article  MATH  Google Scholar 

  15. Goetsche, R., Voxman, W.: Elementary calculus. Fuzzy Sets Syst. 18, 31–43 (1986)

    Article  MathSciNet  Google Scholar 

  16. Ma, M., Friedman, M., Kandel, A.: A new fuzzy arithmetic. Fuzzy Sets Syst. 108, 83–90 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  17. Zimmermann, H.J.: Fuzzy Set Theory and its Applications. Kluwer Academic Press, Dordrecht (1991)

    Book  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  19. Wang, X., Kerre, E.E.: Reasonable properties for the ordering of fuzzy quantities I. Fuzzy Sets Syst. 118, 375–385 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  21. Abbasbandy, S., Asady, B.: Ranking of fuzzy numbers by sign distance. Inform. Sci. 176, 2405–2416 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  22. Asady, B.: The revised method of ranking LR fuzzy number based on deviation degree. Expert Syst. Appl. 37(7), 5056–5060 (2010)

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

  26. Wood, F.: Factors influencing research performance of university academic staff. High. Educ. 19, 81–100 (1990)

    Article  Google Scholar 

  27. Dursun, M., Karsak, E.E.: A fuzzy MCDM approach for personnel selection. Expert Syst. Appl. 37, 4324–4330 (2010)

    Article  Google Scholar 

  28. Chu, T.C., Lin, Y.C.: A fuzzy TOPSIS method for robot selection. Int. J. Adv. Manuf. Technol. 21, 284–290 (2003)

    Article  Google Scholar 

Download references

Acknowledgement

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)

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Luu Quoc Dat.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yu, V.F., Van, L.H., Dat, L.Q. et al. Analyzing the Ranking Method for Fuzzy Numbers in Fuzzy Decision Making Based on the Magnitude Concepts. Int. J. Fuzzy Syst. 19, 1279–1289 (2017). https://doi.org/10.1007/s40815-016-0223-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-016-0223-8

Keywords

Navigation