Revised PROMETHEE algorithm with reference values

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.