Fuzzy Information and Engineering

, Volume 2, Issue 1, pp 37–47 | Cite as

RM approach for ranking of generalized trapezoidal fuzzy numbers

Original Article


Ranking of fuzzy numbers play an important role in decision making, optimization and forecasting etc. Fuzzy numbers must be ranked before an action is taken by a decision maker. In this paper, with the help of several counter examples, it is proved that ranking method proposed by Chen and Chen (Expert Systems with Applications 36 (3): 6833) is incorrect. The main aim of this paper is to propose a new approach for the ranking of generalized trapezoidal fuzzy numbers. The proposed ranking approach is based on rank and mode so it is named as an RM approach. The main advantage of the proposed approach is that the proposed approach provides the correct ordering of generalized and normal trapezoidal fuzzy numbers and also the proposed approach is very simple and easy to apply in the real life problems. It is shown that proposed ranking function satisfies all the reasonable properties of fuzzy quantities proposed by Wang and Kerre (Fuzzy Sets and Systems 118 (3): 375).


Ranking function Generalized trapezoidal fuzzy number 


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  1. 1.
    Abbasbandy S, Hajjari T (2009) A new approach for ranking of trapezoidal fuzzy numbers. Computers and Mathematics with Applications 57(3): 413MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Campos L, Gonzalez A (1989) A subjective approach for ranking fuzzy numbers. Fuzzy Sets and Systems 29(2): 145MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Chen S J, Chen S M (2007) Fuzzy risk analysis based on the ranking of generalized trapezoidal fuzzy numbers. Applied Intelligence 26(1): 1CrossRefGoogle Scholar
  4. 4.
    Chen S M, Chen J H (2009) Fuzzy risk analysis based on ranking generalized fuzzy numbers with different heights and different spreads. Expert Systems with Applications 36(3): 6833CrossRefGoogle Scholar
  5. 5.
    Cheng C H (1998) A new approach for ranking fuzzy numbers by distance method. Fuzzy Sets and Systems 95(3): 307MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Chu T C, Tsao C T (2002) Ranking fuzzy numbers with an area between the centroid point and original point. Computers and Mathematics with Applications 43(1–2): 111MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Deng Y, Liu Q (2005) A TOPSIS-based centroid-index ranking method of fuzzy numbers and its applications in decision making. Cybernetics and Systems 36(6): 581MATHCrossRefGoogle Scholar
  8. 8.
    Dubois D, Prade H (1980) Fuzzy sets and systems, theory and applications. New York: Academic PressMATHGoogle Scholar
  9. 9.
    Jain R (1976) Decision-making in the presence of fuzzy variables. IEEE Transactions on Systems, Man and Cybernetics 6: 698MATHCrossRefGoogle Scholar
  10. 10.
    Kaufmann A, Gupta M M (1988) Fuzzy mathematical models in engineering and management science. Elsevier Science Publishers, Amsterdam, NetherlandsMATHGoogle Scholar
  11. 11.
    Kwang H C, Lee J H (1999) A method for ranking fuzzy numbers and its application to decision making. IEEE Transaction on Fuzzy Systems 7(6): 677CrossRefGoogle Scholar
  12. 12.
    Liang C, Wu J, Zhang J (2006) Ranking indices and rules for fuzzy numbers based on gravity center point. Paper presented at the 6th world Congress on Intelligent Control and Automation, Dalian, China 21–23Google Scholar
  13. 13.
    Liou T S, Wang M J (1992) Ranking fuzzy numbers with integral value. Fuzzy Sets and Systems 50(3): 247CrossRefMathSciNetGoogle Scholar
  14. 14.
    Modarres M, Sadi Nezhad S (2001) Ranking fuzzy numbers by preference ratio. Fuzzy Sets and Systems 118(3): 429MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Wang X, Kerre E E (2001) Reasonable properties for the ordering of fuzzy quantities (I). Fuzzy Sets and Systems 118(3): 375MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Wang Y J, Lee H S (2008) The revised method of ranking fuzzy numbers with an area between the centroid and original points. Computers and Mathematics with Applications 55(9): 2033MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Yager R R (1981) A procedure for ordering fuzzy subsets of the unit interval. Information Sciences 24(2): 143MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Zadeh L A (1965) Fuzzy sets. Information and Control 8(3): 338MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg and Fuzzy Information and Engineering Branch of the Operations Research Society of China 2010

Authors and Affiliations

  1. 1.School of Mathematics and Computer ApplicationsThapar UniversityPatialaIndia

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