Group Decision and Negotiation

, Volume 22, Issue 5, pp 851–866 | Cite as

Type-2 TOPSIS: A Group Decision Problem When Ideal Values are not Extreme Endpoints

  • Majid Zerafat Angiz Langroudi
  • Ali Emrouznejad
  • Adli Mustafa
  • Joshua Ignatius


In the traditional TOPSIS, the ideal solutions are assumed to be located at the endpoints of the data interval. However, not all performance attributes possess ideal values at the endpoints. We termed performance attributes that have ideal values at extreme points as Type-1 attributes. Type-2 attributes however possess ideal values somewhere within the data interval instead of being at the extreme end points. This provides a preference ranking problem when all attributes are computed and assumed to be of the Type-1 nature. To overcome this issue, we propose a new Fuzzy DEA method for computing the ideal values and distance function of Type-2 attributes in a TOPSIS methodology. Our method allows Type-1 and Type-2 attributes to be included in an evaluation system without compromising the ranking quality. The efficacy of the proposed model is illustrated with a vendor evaluation case for a high-tech investment decision making exercise. A comparison analysis with the traditional TOPSIS is also presented.


Multiple attribute decision making (MADM) Fuzzy data envelopment analysis TOPSIS MCDM Group decision making 


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  1. Bal H, Orkcu HH, Celebioglu S (2008) A new method based on the dispersion of weights in data envelopment analysis. Comput Ind Eng 54(3): 502–512CrossRefGoogle Scholar
  2. Barron FH, Barrett BE (1996) Decision quality using ranked attribute weights. Manag Sci 42(11): 1515–1523CrossRefGoogle Scholar
  3. Charnes A, Cooper WW, Rhodes E (1978) Measuring the efficiency of decision making units. Eur J Oper Res 2(6): 429–444CrossRefGoogle Scholar
  4. Deng C, Yeh CH, Willis RJ (2000) Inter-company comparison using modified TOPSIS with objective weights. Comput Oper Res 27(10): 963–973CrossRefGoogle Scholar
  5. Dubois D, Prade H (1987) The mean value of a fuzzy number. Fuzzy Sets Syst 24(3): 279–300CrossRefGoogle Scholar
  6. Golany B (1988) An interactive MOLP procedure for the extension of DEA to effectiveness analysis. J Oper Res Soc 39(8): 725–734Google Scholar
  7. Hatami-Marbini A, Emrouznejad A, Tavana M (2011) A taxonomy and review of the fuzzy data envelopment analysis literature: two decades in the making. Eur J Oper Res 214: 457–472CrossRefGoogle Scholar
  8. Hobbs BF (1978) A comparison of weighting methods in power plant citing. Decis Sci 11(4): 725–737CrossRefGoogle Scholar
  9. Hwang CL, Yoon K (1981) Multiple attribute decision making: methods and applications. Springer, New York, NYCrossRefGoogle Scholar
  10. Lai YJ, Hwang CL (1992) Fuzzy mathematical programming: methods and applications. Springer, New York, NYCrossRefGoogle Scholar
  11. Li XB, Reeves GR (1999) A multiple criteria approach to data envelopment analysis. Eur J Oper Res 115(3): 507–517CrossRefGoogle Scholar
  12. Lins MPE, DeLyra Novaes LF, Legey LFL (2005) Real estate appraisal: a double perspective data envelopment analysis approach. Ann Oper Res 138(1): 79–96CrossRefGoogle Scholar
  13. Saati MS, Zarafat Angiz LM, Memariani A, Jahanshahloo GR (2001) A model for ranking decision making units in data envelopment analysis. Ricerca Operativa 31(97): 47–59Google Scholar
  14. Schoemaker PJH, Waid CD (1982) An experimental comparison of different approaches to determining weights in additive utility models. Manag Sci 28(2): 182–196CrossRefGoogle Scholar
  15. Soaresde Mello JCCB, Gomes EG, Angulo-Meza L, Leta FR (2008) DEA advanced models for geometric evaluation of used lathes. WSEAS Trans Syst 7(5): 500–520Google Scholar
  16. Wang YM, Luo Y (2009) A note on a new method based on the dispersion of weights in data envelopment analysis. Comput Ind Eng 56(4): 1703–1707CrossRefGoogle Scholar
  17. Wu D (2006) A note on DEA efficiency assessment using ideal point: an improvement of Wang and Luo’s model. Appl Math Comput 183(2): 819–830CrossRefGoogle Scholar
  18. Yamada Y, Matsui T, Sugiyama M (1994) An inefficiency measurement method for management systems. J Oper Res Soc Jpn 37: 158–167Google Scholar
  19. Yeh CH, Chang YH (2009) Modeling subjective evaluation for fuzzy group multi-criteria decision making. Eur J Oper Res 194(2): 464–473CrossRefGoogle Scholar
  20. Zarafat Angiz ML, Saati MS, Memariani A, Movahedi M (2006) Solving possibilistic linear programming problem considering membership function of the coefficients. Adv Fuzzy Sets Syst 1(2): 131–142Google Scholar
  21. Zeleny M (1982) Multiple criteria decision making. McGraw-Hill, New York, NYGoogle Scholar
  22. Zerafat Angiz LM, Emrouznejad A, Mustafa A, Rashidi Komijan A (2009) Selecting the most preferable alternatives in a group decision making problem using DEA. Expert Syst Appl 36(5): 9599–9602CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Majid Zerafat Angiz Langroudi
    • 1
  • Ali Emrouznejad
    • 2
  • Adli Mustafa
    • 1
  • Joshua Ignatius
    • 1
  1. 1.School of Mathematical SciencesUniversiti Sains MalaysiaPenangMalaysia
  2. 2.Aston Business SchoolAston UniversityBirminghamUK

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