A new algorithm for synthesising locally most consistent priorities in analytic hierarchy process for group decision making

Abstract

The analytic hierarchy process (AHP) is an efficient tool in supporting group decision making processes because it is offering various possibilities to aggregate individual opinions, judgments and/or priorities into group equivalents, allowing control over the consistency of participating individuals. This paper proposes a straightforward procedure to locally identify: 1) the most consistent decision maker; 2) an associated prioritisation method; 3) the corresponding best local priority vector (set of weights in given node of hierarchy), to be used for the final AHP synthesis. Minimum total Euclidean distance as a universal consistency measure for the hierarchy is guaranteed on the group of decision makers and on a set of most used matrix and optimisation prioritisation methods. The algorithm is named as AHP-DPE and is applicable to any complete hierarchy (which is a philosophical pillar of AHP), for any size of a group and for any number of prioritisation methods. Selected example from agriculture illustrates how proposed methodology can be efficiently applied to obtain trustful solution in the group decision making context.