Fuzzy assessment of priorities with application to competitive bidding

A new fuzzy preference programming method for deriving priorities from inconsistent interval pairwise comparison matrices in the Analytical Hierarchy Process is presented, which represents the inconsistent interval judgements as fuzzy linear constraints and defines a convex non—empty fuzzy feasible area.

Abstract

ABSTRACT This paper presents a new fuzzy preference programming method for deriving priorities from inconsistent interval pairwise comparison matrices in the Analytical Hierarchy Process (AHP). The preference programming method of Arbel for elicitation of the priorities from interval matrices transforms the prioritisation problem into a linear program, which is attractive from a computational point of view, however it cannot deal with inconsistent decision—maker judgements. The proposed fuzzy preference programming method represents the inconsistent interval judgements as fuzzy linear constraints and defines a convex non—empty fuzzy feasible area. The assessment of the priorities is stated as an optimisation problem, maximising the decision-maker's satisfaction with the solution of an approximate fuzzy programming problem. The new method is applicable for both crisp and interval inconsistent judgements and can be considered as a generalisation of the classical prioritisation methods in the AHP. An application of this method for the modelling of uncertain judgements and the assessment of priorities in competitive bidding is described.