Interval judgments and Euclidean centers

We formulated the problem of finding a priority vector from an interval reciprocal matrix as a Euclidean center problem. The interesting result is that this formulation always has a solution and always provides knowledge about the feasible region. The sign of the objective function of the Euclidean center formulation predicts the existence of a feasible solution that satisfies the constraints given by the interval reciprocal matrix. We showed that if the Euclidean center objective function is positive, there are multiple plausible solutions, if it is negative, there no feasible solutions, and if it is equal to zero, the feasible region consists of a single point.