Soft Computing

, Volume 15, Issue 7, pp 1373–1381 | Cite as

RM approach for ranking of LR type generalized fuzzy numbers

  • Amit Kumar
  • Pushpinder Singh
  • Parmpreet Kaur
  • Amarpreet Kaur
Original Paper


Ranking of fuzzy numbers play an important role in decision making, optimization, 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 Syst Appl 36:6833–6842, 2009) is incorrect. The main aim of this paper is to propose a new approach for the ranking of LR type generalized fuzzy numbers. The proposed ranking approach is based on rank and mode so it is named as RM approach. The main advantage of the proposed approach is that it provides the correct ordering of generalized and normal fuzzy numbers and it 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 Syst 118:375–385, 2001).


Ranking function LR type generalized fuzzy number 


  1. Abbasbandy S, Hajjari T (2009) A new approach for ranking of trapezoidal fuzzy numbers. Comput Math Appl 57:413–419MathSciNetCrossRefMATHGoogle Scholar
  2. Campos LM, Gonzalez A (1989) A subjective approach for ranking fuzzy numbers. Fuzzy Sets Syst 29:145–153CrossRefMATHGoogle Scholar
  3. Chen SJ, Chen SM (2007) Fuzzy risk analysis based on the ranking of generalized trapezoidal fuzzy numbers. Appl Intell 26:1–11CrossRefGoogle Scholar
  4. Chen SM, Chen JH (2009) Fuzzy risk analysis based on ranking generalized fuzzy numbers with different heights and different spreads. Expert Syst Appl 36:6833–6842CrossRefGoogle Scholar
  5. Chen CC, Tang HC (2008) Ranking nonnormal p-norm trapezoidal fuzzy numbers with integral value. Comput Math Appl 56:2340–2346MathSciNetCrossRefMATHGoogle Scholar
  6. Chen SM, Wang CH (2009) Fuzzy risk analysis based on ranking fuzzy numbers using α-cuts, belief features and signal/noise ratios. Expert Syst Appl 36:5576–5581CrossRefGoogle Scholar
  7. Cheng CH (1998) A new approach for ranking fuzzy numbers by distance method. Fuzzy Sets Syst 95:307–317CrossRefMATHGoogle Scholar
  8. Chu TC, Tsao CT (2002) Ranking fuzzy numbers with an area between the centroid point and original point. Comput Math Appl 43:111–117MathSciNetCrossRefMATHGoogle Scholar
  9. Deng Y, Liu Q (2005) A TOPSIS-based centroid-index ranking method of fuzzy numbers and its applications in decision making. Cybern Syst 36:581–595CrossRefMATHGoogle Scholar
  10. Jain R (1976) Decision-making in the presence of fuzzy variables. IEEE Trans Syst Man Cybern 6:698–703CrossRefMATHGoogle Scholar
  11. Kaufmann A, Gupta MM (1988) Fuzzy mathematical models in engineering and managment science. Elseiver. AmsterdamGoogle Scholar
  12. Kwang HC, Lee JH (1999) A method for ranking fuzzy numbers and its application to decision making. IEEE Trans Fuzzy Syst 7:677–685CrossRefGoogle Scholar
  13. Liou TS, Wang MJ (1992) Ranking fuzzy numbers with integral value. Fuzzy Sets Syst 50:247–255MathSciNetCrossRefGoogle Scholar
  14. Modarres M, Sadi-Nezhad S (2001) Ranking fuzzy numbers by preference ratio. Fuzzy Sets Syst 118:429–436MathSciNetCrossRefMATHGoogle Scholar
  15. Ramli N, Mohamad D (2009) A comparative analysis of centroid methods in ranking fuzzy numbers. Eur J Sci Res 28:492–501Google Scholar
  16. Wang X, Kerre EE (2001) Reasonable properties for the ordering of fuzzy quantities (I). Fuzzy Sets Syst 118:375–385MathSciNetCrossRefMATHGoogle Scholar
  17. Wang YJ, Lee HS (2008) The revised method of ranking fuzzy numbers with an area between the centroid and original points. Comput Math Appl 55:2033–2042MathSciNetCrossRefMATHGoogle Scholar
  18. Yager RR (1981) A procedure for ordering fuzzy subsets of the unit interval. Inf Sci 24:143–161MathSciNetCrossRefMATHGoogle Scholar
  19. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Amit Kumar
    • 1
  • Pushpinder Singh
    • 1
  • Parmpreet Kaur
    • 1
  • Amarpreet Kaur
    • 1
  1. 1.School of Mathematics and Computer ApplicationsThapar UniversityPatialaIndia

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