Ranking Alternatives by Pairwise Comparisons Matrix with Fuzzy Elements on Alo-Group

The decision making problem considered in this paper is to rank n alternatives from the best to the worst, using the information given by the decision maker in the form of an n by n pairwise comparisons matrix. Here, we deal with a pairwise comparisons matrix with fuzzy elements (PCF matrix). Fuzzy elements of the pairwise comparisons matrix are applied whenever the decision maker is not sure about the value of his/her evaluation, or, the elements of the PCF matrix are aggregated crisp evaluations in a group decision making problem. We investigate pairwise comparisons matrices with elements from an abelian linearly ordered group (alo-group) over a real interval. We propose a method starting from construction of fuzzy elements of a reciprocal PCF matrix, calculating its consistency and resulting into computation of the priority vector associated to the ranking of the alternatives. Illustrating examples are presented and discussed.