Abstract
The technique for order preference by similarity to ideal solution (TOPSIS) is a widely used ranking method which provides a composite index representing the relative proximity of each decision alternative to an ideal solution. The relative proximity index construction relays on the use of a single criterion aggregation approach. Its output, regardless the certainty or uncertainty nature of the problem’s data, is usually a real number. In TOPSIS classical approach alternatives are ordered based on these numbers. The closer the number to 1, the higher the position of the alternative in the ranking. However, although the relative proximity index can be highly sensible to the weighting scheme, as far as the authors of this work know, the relative proximity index has never been treated as a function. In this work, a new TOPSIS approach is proposed in which weights are not fixed in an exact way a priori. On the contrary, they are handled as decision variables in a set of optimization problems where the objective is to maximize the relative proximity of each alternative to the ideal solution. The only possible a priori information about the weights is that related to the existence of upper and lower bounds in their values. This information is incorporated into the optimization problems as constraints. The result is a new relative proximity index which is a function depending on the values of the weights. This feature of the proposed method could be useful in some decision situations in which the determination of subjective precise weights from decision makers could be problematic.
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28 July 2020
A Correction to this paper has been published: https://doi.org/10.1007/s10479-020-03738-x
Notes
In addition to the vector normalization proposed in the seminal paper by Hwang and Yoon, many other normalization processes have been used (Ouenniche et al. 2018).
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Acknowledgements
This work has been supported by the Spanish Ministerio de Ciencia, Innovación y Universidades, project reference number: RTI2018-093541-B-I00. The authors would like to sincerely thank Equileap for the provision of the data in the case study and for all their comments and suggestions. We would also like to thank the anonymous referees for all their detailed comments which have improved the quality and clarity of this work.
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Appendix
Appendix
Tables 17, 18 and 19 show the values of the weights providing the maximum and minimum Ri in Examples 1, 2 and the Case Study, respectively. In all cases, the optimization problems have been solved with LINGO.
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Liern, V., Pérez-Gladish, B. Multiple criteria ranking method based on functional proximity index: un-weighted TOPSIS. Ann Oper Res 311, 1099–1121 (2022). https://doi.org/10.1007/s10479-020-03718-1
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DOI: https://doi.org/10.1007/s10479-020-03718-1