Ranking Alternatives Using QUALIFLEX Method by Computing All Spanning Trees from Pairwise Judgements

QUALIFLEX, a well-known outranking method based on Jacquet-Lagreze’s permutation method, investigates all possible permutations of alternatives in order to find the final decision result. It is worthy to mention that to choose the best ranking order, it is not required to always consider total m! permutations of the ranking order of alternatives if the number of alternatives is m. This drawback of QUALIFLEX of implanting the huge computations for all permutations of alternatives motivates us to develop a new ranking method. In our proposed ranking method, the algorithmic complexity of QUALIFLEX method is overcome by generating only the possible preference orders of alternatives from the set of judgements, which are in the form of real data, using graph theoretic approach. Then we calculate the concordance and discordance indices in the desired sets of preferences and finally choose the ultimate alternative. Furthermore, an example is provided to illustrate the application of the proposed method, together with comparison analysis.