Skip to main content

TOPSIS

  • Chapter
  • First Online:
Multiple Criteria Decision Aid

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 136))

Abstract

TOPSIS is an acronym that stands for ‘Technique of Order Preference Similarity to the Ideal Solution’ and is a pretty straightforward MCDA method. As the name implies, the method is based on finding an ideal and an anti-ideal solution and comparing the distance of each one of the alternatives to those. It was presented in Hwang and Yoon (Multiple attribute decision making: methods and applications. Springer, Berlin, 1981) and Chen and Hwang (Fuzzy multiple attribute decision making methods. Springer, Berlin, 1992), and can be considered as one of the classical MCDA methods that has received a lot of attention from scholars and researchers. It has been successfully applied in various instances; for a comprehensive state-of-the-art literature review, refer to Behzadian et al. (Expert Syst Appl 39(17):13051–13069, 2012). Table 1.1, adopted from that reference, presents the distribution of papers on TOPSIS by application areas.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Anisseh, M., Piri, F., Shahraki, M. R., & Agamohamadi, F. (2012). Fuzzy extension of TOPSIS model for group decision making under multiple criteria. Artificial Intelligence Review, 38(4), 325–338.

    Article  Google Scholar 

  2. Bede, B. (2013). Mathematics of fuzzy sets and fuzzy logic. Berlin: Springer.

    Book  Google Scholar 

  3. Behzadian, M., Otaghsara, S. K., Yazdani, M., & Ignatius, J. (2012). A state-of the-art survey of TOPSIS applications. Expert Systems with Applications, 39(17), 13051–13069.

    Article  Google Scholar 

  4. Cha, Y., & Jung, M. (2003). Satisfaction assessment of multi-objective schedules using neural fuzzy methodology. International Journal of Production Research, 41(8), 1831–1849.

    Article  Google Scholar 

  5. Chen, C. T. (2000). Extensions of the TOPSIS for group decision-making under fuzzy environment. Fuzzy Sets and Systems, 114, 1–9.

    Article  Google Scholar 

  6. Chen, S. H. (1985). Ranking fuzzy numbers with maximizing set and minimizing set. Fuzzy Sets and Systems, 17(2), 113–129.

    Article  MathSciNet  Google Scholar 

  7. Chen, S. J., & Hwang, C. L. (1992). Fuzzy multiple attribute decision making methods. Berlin: Springer.

    Book  Google Scholar 

  8. Chu, T. C. (2002). Facility location selection using fuzzy TOPSIS under group decisions. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 10(6), 687–701.

    Article  MathSciNet  Google Scholar 

  9. Chu, T. C., & Lin, Y. C. (2003). A fuzzy TOPSIS method for robot selection. The International Journal of Advanced Manufacturing Technology, 21(4), 284–290.

    Article  Google Scholar 

  10. Diamond, P., & Kloeden, P. (2000). Metric topology of fuzzy numbers and fuzzy analysis. In D. Dubois & H. Prade (Eds.), Fundamentals of fuzzy sets (pp. 583–641). New York: Springer US.

    Chapter  Google Scholar 

  11. Dymova, L., Sevastjanov, P., & Tikhonenko, A. (2013). An approach to generalization of fuzzy TOPSIS method. Information Sciences, 238, 149–162.

    Article  MathSciNet  Google Scholar 

  12. Garcia-Cascales, M. S., & Lamata, M. T. (2012). On rank reversal and TOPSIS method. Mathematical and Computer Modelling, 56(5), 123–132.

    Article  MathSciNet  Google Scholar 

  13. Giove, S. (2002). Interval TOPSIS for multicriteria decision making. In Italian Workshop on Neural Nets (pp. 56–63). Berlin: Springer.

    Chapter  Google Scholar 

  14. Hwang, C. L., & Yoon, K. (1981). Multiple attribute decision making: Methods and applications. Berlin: Springer

    Book  Google Scholar 

  15. Izadikhah, M. (2009). Using the Hamming distance to extend TOPSIS in a fuzzy environment. Journal of Computational and Applied Mathematics, 231(1), 200–207.

    Article  MathSciNet  Google Scholar 

  16. Jahan, A., & Edwards, K. L. (2015). A state-of-the-art survey on the influence of normalization techniques in ranking: Improving the materials selection process in engineering design. Materials & Design, 65, 335–342.

    Article  Google Scholar 

  17. Jahanshahloo, G. R., Lotfi, F. H., & Davoodi, A. R. (2009). Extension of TOPSIS for decision-making problems with interval data: interval efficiency. Mathematical and Computer Modelling, 49(5), 1137–1142.

    Article  MathSciNet  Google Scholar 

  18. Jahanshahloo, G. R., Lotfi, F. H., & Izadikhah, M. (2006). An algorithmic method to extend TOPSIS for decision-making problems with interval data. Applied Mathematics and Computation, 175(2), 1375–1384.

    Article  Google Scholar 

  19. Jahanshahloo, G. R., Lotfi, F. H., & Izadikhah, M. (2006). Extension of the TOPSIS method for decision-making problems with fuzzy data. Applied Mathematics and Computation, 181(2), 1544–1551.

    Article  Google Scholar 

  20. Kahraman, C., Kaya, I., Çevik, S., Ates, N. Y., & Gülbay, M. (2008). Fuzzy multi-criteria evaluation of industrial robotic systems using TOPSIS. In C. Kahramn (Ed.), Fuzzy multi-criteria decision making (pp. 159–186). New York: Springer US.

    Chapter  Google Scholar 

  21. Kaufmann, A., & Gupta, M. M. (1988). Fuzzy mathematical models in engineering and management science. New York: Elsevier Science Inc.

    MATH  Google Scholar 

  22. Lee, E. S., & Li, R. J. (1988). Comparison of fuzzy numbers based on the probability measure of fuzzy events. Computers & Mathematics with Applications, 15(10), 887–896.

    Article  MathSciNet  Google Scholar 

  23. Lee, K. H. (2006). First course on fuzzy theory and applications (Vol. 27). Berlin: Springer Science & Business Media.

    Google Scholar 

  24. Li, X., & Chen, X. (2014). Extension of the TOPSIS method based on prospect theory and trapezoidal intuitionistic fuzzy numbers for group decision making. Journal of Systems Science and Systems Engineering, 23(2), 231–247.

    Article  MathSciNet  Google Scholar 

  25. Liang, G. S. (1999). Fuzzy MCDM based on ideal and anti-ideal concepts. European Journal of Operational Research, 112(3), 682–691.

    Article  Google Scholar 

  26. Liou, T. S., & Wang, M. J. J. (1992). Ranking fuzzy numbers with integral value. Fuzzy Sets and Systems, 50(3), 247–255.

    Article  MathSciNet  Google Scholar 

  27. Mahdavi, I., Mahdavi-Amiri, N., Heidarzade, A., & Nourifar, R. (2008). Designing a model of fuzzy TOPSIS in multiple criteria decision making. Applied Mathematics and Computation, 206(2), 607–617.

    Article  MathSciNet  Google Scholar 

  28. Owen, S. H., & Daskin, M. S. (1998). Strategic facility location: A review. European Journal of Operational Research, 111(3), 423–447.

    Article  Google Scholar 

  29. Pavlicic, D. (2001). Normalization affects the results of MADM methods. Yugoslav Journal of Operations Research, 11(2), 251–265.

    MATH  Google Scholar 

  30. ReVelle, C. S., & Eiselt, H. A. (2005). Location analysis: a synthesis and survey. European Journal of Operational Research, 165(1), 1–19.

    Article  MathSciNet  Google Scholar 

  31. Shih, H. S., Shyur, H. J., & Lee, E. S. (2007). An extension of TOPSIS for group decision making. Mathematical and Computer Modelling, 45(7), 801–813.

    Article  Google Scholar 

  32. Tsaur, S. H., Chang, T. Y., & Yen, C. H. (2002). The evaluation of airline service quality by fuzzy MCDM. Tourism Management, 23(2), 107–115.

    Article  Google Scholar 

  33. Vafaei, N., Ribeiro, R. A., & Camarinha-Matos, L. M. (2015). Importance of data normalization in decision making: Case study with TOPSIS method. In B. Delibasic, F. Dargam, P. Zarate, J.E. Hernendez, S. Liu, R. Ribeiro, I. Linden & J. Papathanasiou (Eds.), ICDSST 2015 Proceedings - the 1st International Conference on Decision Support Systems Technologies, an EWG-DSS Conference, Belgrade, Serbia.

    Google Scholar 

  34. Wang, T. C., & Lee, H. D. (2009). Developing a fuzzy TOPSIS approach based on subjective weights and objective weights. Expert Systems with Applications, 36(5), 8980–8985.

    Article  Google Scholar 

  35. Wang, Y. J., & Lee, H. S. (2007). Generalizing TOPSIS for fuzzy multiple-criteria group decision-making. Computers & Mathematics with Applications, 53(11), 1762–1772.

    Article  MathSciNet  Google Scholar 

  36. Wang, Y. M., & Elhag, T. M. (2006). Fuzzy TOPSIS method based on alpha level sets with an application to bridge risk assessment. Expert Systems with Applications, 31(2), 309–319.

    Article  Google Scholar 

  37. Wang, Y. M., & Luo, Y. (2009). On rank reversal in decision analysis. Mathematical and Computer Modelling, 49(5), 1221–1229.

    Article  MathSciNet  Google Scholar 

  38. Yang, T., & Hung, C. C. (2007). Multiple-attribute decision making methods for plant layout design problem. Robotics and Computer-Integrated Manufacturing, 23(1), 126–137.

    Article  Google Scholar 

  39. Yue, Z. (2012). Extension of TOPSIS to determine weight of decision maker for group decision making problems with uncertain information. Expert Systems with Applications, 39(7), 6343–6350.

    Article  Google Scholar 

  40. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353.

    Article  MathSciNet  Google Scholar 

  41. Zadeh, L. A. (1975). The concept of a linguistic variable and its application to approximate reasoning—I. Information Sciences, 8(3), 199–249.

    Article  MathSciNet  Google Scholar 

  42. Zhang, G., & Lu, J. (2003). An integrated group decision-making method dealing with fuzzy preferences for alternatives and individual judgements for selection criteria. Group Decision and Negotiation, 12(6), 501–515.

    Article  Google Scholar 

  43. Zhao, R., & Govind, R. (1991). Algebraic characteristics of extended fuzzy numbers. Information Sciences, 54(1), 103–130.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

1.1 Electronic Supplementary Material

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Papathanasiou, J., Ploskas, N. (2018). TOPSIS. In: Multiple Criteria Decision Aid . Springer Optimization and Its Applications, vol 136. Springer, Cham. https://doi.org/10.1007/978-3-319-91648-4_1

Download citation

Publish with us

Policies and ethics