A goal programming and analytic hierarchy process method for solving group decision-making fuzzy AHP problems

The analytic hierarchy process (AHP) elicits a corresponding priority vector interpreting the preferred information from the decision-maker(s), based on the pairwise comparison values of a set of objects. Since pairwise comparison values are the judgments obtained from an appropriate semantic scale, in practice the decision-maker(s) usually give some or all pair-to-pair comparison values with an uncertainty degree rather than precise ratings. By employing the property of goal programming (GP) to treat a fuzzy AHP problem, this paper incorporates an absolute term linearization technique and a fuzzy rating expression into a GP-AHP model for solving group decision-making fuzzy AHP problems. In contrast to current fuzzy AHP methods, the GP-AHP method developed herein can concurrently tackle the pairwise comparison involving triangular, general concave and concave–convex mixed fuzzy estimates under a group decision-making environment.