A new AHP‐prioritization method based on linear programming for crisp and interval preference relations

Abstract Obtaining a priority (weight) vector is a crucial topic in the analytic hierarchy process (AHP). This paper proposes a novel prioritization approach based on linear programming (LP) for obtaining priorities in the AHP. We apply this approach to group decision making and modify it to include uncertainty in the decision maker's subjective judgments when the pairwise comparison matrix (PCM) elements are intervals. The proposed LP approach has a high potential in ranking the elements (decision criteria or alternatives). It is always feasible and produces interval priority vectors with positive lower and upper bounds for interval PCMs. These are important advantages of the proposed model in comparison to some existing models. To illustrate the potential applications and advantages of this approach, some numerical examples, including a multiple criteria decision making problem with a hierarchical structure, are examined.