Review and the Use of PROMETHEE Methods in Marketing (Problems)

2. Promethee Ii Overview And Description

This section briefly describes PROMETHEE II, which is intended to provide a complete ranking of a finite set of feasible alternatives from the best to the worst. This method is fundamental to implement the other PROMETHEE methods and the majority of researchers have referred to this version of the PROMETHEE methods. The basic principle of PROMETHEE II is based on a pairwise comparison of alternatives along each recognized criterion. Alternatives are evaluated according to different criteria, which have to be maximized or minimized. The implementation of the PROMETHEE II requires the determination of the weight PROMETHEE II assumes that the decision-maker is able to weigh the criteria appropriately, at least when the number of criteria is not too large (Macharis et al., 2004). Additionally, it requires the selection of the preference function for each criterion, so to translate the difference between the evaluations obtained by two alternatives into a preference degree ranging from zero to one. In order to facilitate the selection of a specific preference function, Vincke and Brans (1985) proposed six basic types: (1) usual criterion, (2) U-shape criterion, (3) V-shape criterion, (4) level criterion, (5) V-shape with indifference criterion and (6) Gaussian criterion. These six types are particularly easy to define. For each criterion, the value of an indifference threshold, q; the value of a strict preference threshold, p; and the value of an intermediate value between p and q, s, has to be fixed (Brans and Mareschal, 1992). In each case, these parameters have a clear significance for the decision-maker. The procedure is started to determine deviations based on pair-wise comparisons. It is followed by using a relevant preference function for each criterion in Step 2, calculating global preference index in Step 3, and calculating positive and negative outranking flows for each alternative and partial ranking in Step 4. The procedure is come to an end with the calculation of net outranking flow for each alternative and complete ranking.

The PROMETHEE method includes the outranking evaluations, applying different mechanisms. It includes the PROMETHEE I for partial ranking of the alternatives and the PROMETHEE II for complete ranking of the alternatives. The specific mechanisms were initial built by Brans in 1982 at a conference organized at the University Laval, Quebec, Canada (Brans, 1982, Mareschal, 1986). Later on, it was included the mechanism of: