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Revised PROMETHEE algorithm with reference values

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  • František Zapletal

    (VŠB-Technical University of Ostrava)

Abstract

PROMETHEE method is a very popular quantitative method of decision-making with many benefits. However, the evaluation of alternatives in the original PROMETHEE method is derived only from differences in values, i.e., regardless the performance values themselves. In some situations, ignoring these values can distort the final results. This paper brings several examples of such situations, for which the original PROMETHEE fails and does not bring reliable results. Ishizaka and Resce (Soft Comput 22:7325–7338, 2018) have recently introduced the modification of PROMETHEE which considers the performance values, but also changed substantially the logic of the ranking algorithm. The aim of this paper is to modify the original PROMETHEE method to make it possible to include the performance values, without losing any main benefit of the original method and with keeping the original logic of the algorithm based on pair-wise comparisons. Two particular preference functions’ types are proposed for the proposed extension (Gaussian function and strictly concave function), whose choice depends on the performance of the worst-performing alternative under consideration. In addition, the new algorithm is provided also in the fuzzy environment, which is useful if the decision-maker is not able to set the input parameters of the preference function precisely. Both the deterministic and fuzzy extensions are demonstrated using numerical examples. The results show that the final ranking can be strongly influenced by the level of performance. Moreover, the fuzzy extension brings richer information through the natural interpretation provided by possibility and necessity measures if the parameters of the preference functions are imprecise.

Suggested Citation

  • František Zapletal, 2022. "Revised PROMETHEE algorithm with reference values," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 30(2), pages 521-545, June.
    • Handle: RePEc:spr:cejnor:v:30:y:2022:i:2:d:10.1007_s10100-021-00767-0
    DOI: 10.1007/s10100-021-00767-0
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    References listed on IDEAS

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    1. Ishizaka, Alessio & Resce, Giuliano, 2021. "Best-Worst PROMETHEE method for evaluating school performance in the OECD's PISA project," Socio-Economic Planning Sciences, Elsevier, vol. 73(C).
    2. Bruce R. Beattie & Jeffrey T. LaFrance, 2006. "The Law of Demand versus Diminishing Marginal Utility," Review of Agricultural Economics, Agricultural and Applied Economics Association, vol. 28(2), pages 263-271.
    3. Goumas, M. & Lygerou, V., 2000. "An extension of the PROMETHEE method for decision making in fuzzy environment: Ranking of alternative energy exploitation projects," European Journal of Operational Research, Elsevier, vol. 123(3), pages 606-613, June.
    4. Ishizaka, Alessio & Lokman, Banu & Tasiou, Menelaos, 2021. "A Stochastic Multi-criteria divisive hierarchical clustering algorithm," Omega, Elsevier, vol. 103(C).
    5. Céline Verly & Yves De Smet, 2013. "Some results about rank reversal instances in the PROMETHEE methods," International Journal of Multicriteria Decision Making, Inderscience Enterprises Ltd, vol. 3(4), pages 325-345.
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