Deriving priorities from fuzzy pairwise comparison judgements

Abstract

A new approach for deriving priorities from fuzzy pairwise comparison judgements is proposed, based on α-cuts decomposition of the fuzzy judgements into a series of interval comparisons. The assessment of the priorities from the pairwise comparison intervals is formulated as an optimisation problem, maximising the decision-maker's satisfaction with a specific crisp priority vector. A fuzzy preference programming method, which transforms the interval prioritisation task into a fuzzy linear programming problem is applied to derive optimal crisp priorities. Aggregating the optimal priorities, which correspond to different α-cut levels enables overall crisp scores of the prioritisation elements to be obtained. A modification of the linear fuzzy preference programming method is also proposed to derive priorities directly from fuzzy judgements, without applying α-cut transformations. The formulation of the prioritisation problem as an optimisation task is similar to the previous approach, but it requires the solution of a non-linear optimisation program. The second approach also derives crisp priorities and has the advantage that it does not need additional aggregation and ranking procedures. Both proposed methods are illustrated by numerical examples and compared to some of the existing fuzzy prioritisation methods.