On the Normalization of a Priority Vector Associated with a Reciprocal Relation

In this paper, we show that the widely used normalisation constraint requiring that the entries of a vector sum up to one does not apply to the priority vectors associated with reciprocal relations, also called fuzzy preference relations, whenever additive transitivity is involved. We show that misleading applications of this type of normalisation may lead to unsatisfactory results and we give some examples from the literature. Then, we propose an alternative normalisation procedure which is compatible with additive transitivity and leads to better results.