A fuzzy approach to deriving priorities from interval pairwise comparison judgements

In this paper we study the problem of priority elicitation in the analytic hierarchy process and propose a new approach to deriving crisp priorities from interval pairwise comparison judgements. By introducing linear or non-linear membership functions, representing the decision-maker's degree of satisfaction with various crisp priority vectors, the interval judgements are transformed into fuzzy inequality constraints. The interval prioritisation problem is then formulated as a fuzzy mathematical programming problem for obtaining an optimal crisp priority vector that maximises the overall degree of satisfaction. The proposed approach yields linear or non-linear mathematical programs, capable of deriving priorities from consistent and inconsistent interval judgements. The presence of a consistency index that measures the level of inconsistency of interval judgements is an attractive feature of our approach. Another feature, which does not exist in the known prioritisation methods, is the opportunity for additional priorisation of the initial judgements. Numerical examples are given and comparisons with other interval prioritisation methods are carried out.