Some issues on consistency of fuzzy preference relations

In decision making, in order to avoid misleading solutions, the study of consistency when the decision makers express their opinions by means of preference relations becomes a very important aspect in order to avoid misleading solutions. In decision making problems based on fuzzy preference relations the study of consistency is associated with the study of the transitivity property. In this paper, a new characterization of the consistency property defined by the additive transitivity property of the fuzzy preference relations is presented. Using this new characterization a method for constructing consistent fuzzy preference relations from a set of n-1 preference data is proposed. Applying this method it is possible to assure better consistency of the fuzzy preference relations provided by the decision makers, and in such a way, to avoid the inconsistent solutions in the decision making processes. Additionally, a similar study of consistency is developed for the case of multiplicative preference relations.