Ranking Alternatives under FWA by Riemann Integral Based Mean of Removals

Conference paper
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 15)


This paper suggests developing membership functions of the final fuzzy evaluation values of alternatives under fuzzy weighted average (FWA), where ratings of alternatives versus qualitative criteria and the importance weights of all criteria are assessed in linguistic values represented by fuzzy numbers. Ranking approach of Riemann integral based mean of removals is applied to solve defuzzification to complete the model. Solving square root of affected quadratic equation through Riemann integral in using mean of removals for obtaining the integral values under membership functions from FWA will be studied. Formulae of ranking approach can be clearly developed, making computation execution of the proposed model more efficient. A numerical example has demonstrated feasibility of the proposed model.


Ranking FWA Riemann integral Mean of removals 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abbasbandy, S., Hajjari, T.: A new approach for ranking of trapezoidal fuzzy numbers. Computers and Mathematics with Applications 57(3), 413–419 (2009)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Asady, B.: Revision of distance minimization method for ranking of fuzzy numbers. Applied Mathematical Modeling 35, 1306–1313 (2011)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Chen, C.T.: A fuzzy approach to select the location of the distribution center. Fuzzy Sets and Systems 118(1), 65–73 (2001)MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Chu, T.C., Lin, Y.: An extension to fuzzy MCDM. Computers and Mathematics with Applications 57(3), 445–454 (2009)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Dong, W.M., Wang, F.S.: Fuzzy weighted averages and implementation of the extension principle. Fuzzy Sets and Systems 21(2), 183–199 (1987)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Dubois, D., Prade, H.: Operation on fuzzy number. International Journal of System Science 9(6), 613–626 (1978)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Dursun, M., Karsak, E.E.: A fuzzy MCDM approach for personnel selection. Expert Systems with Applications 37(6), 4324–4330 (2010)CrossRefGoogle Scholar
  8. 8.
    Guh, Y.Y., Hon, C.C., Wang, K.M., Lee, E.S.: Fuzzy weighted average: a max-min paired elimination method. Computers and Mathematics with Applications 32(8), 115–123 (1996)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Guu, S.M.: The fuzzy weighted average method revisited. Fuzzy Sets and Systems 126(3), 411–414 (2002)MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Kao, C., Liu, S.-T.: Fractional programming approach to fuzzy weighted average. Fuzzy Sets and Systems 120(3), 435–444 (2001)MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    Kaufmann, A., Gupta, M.M.: Introduction to fuzzy arithmetic-theory and application. Van Nostrand Reinhold, New York (1991)Google Scholar
  12. 12.
    Lee, D.H., Park, D.: An efficient algorithm for fuzzy weighted average. Fuzzy Sets and Systems 87(1), 39–45 (1997)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Liou, T.-S., Wang, M.-J.: Fuzzy weighted average: an improved algorithm. Fuzzy Sets and Systems 49(3), 307–315 (1992)MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Momeni, M., Maleki, M.H., Afshari, M.A., Moradi, J.S., Mohammadi, J.: A fuzzy MCDM approach for evaluating listed private banks in Tehran Stock Exchange based on balanced scorecard. International Journal of Business Administration 2(1), 80–97 (2011)Google Scholar
  15. 15.
    Math, S.O.S.: Integrals containing the square root of ax2+bx+c (2008),
  16. 16.
    Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning. Information Sciences 8(3), 199–249 (I), 301–357 (II) (1975)MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Zadeh, L.A.: Fuzzy sets. Information and Control 8(3), 338–353 (1965)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Graduate Institute of Industrial Management, Department of Business AdministrationSouthern Taiwan UniversityTainanTaiwan
  2. 2.Department of Business AdministrationSouthern Taiwan UniversityTainanTaiwan

Personalised recommendations