Determination of local and global weights of alternatives from inconsistent interval judgement matrices

The Analytic Hierarchy Process (AHP) finds out the ‘best’ alternative out of several ones by considering a number of conflicting criteria. In the traditional AHP, the strength of preference of one alternative (or criterion) over another is specified by means of a single number taken from the (1-9) ratio-scale. But in some realistic situations, where outcomes are uncertain, interval judgements may be more appropriate. Taking this into account, local as well as global weights of alternatives are obtained by simulation technique based on three different probability distributions, namely, uniform, truncated normal, and truncated gamma. Subsequently, the effect of these distributions on the two sets of weights is investigated by means of statistical analysis. Then, pointing out the difficulties in the simulation approach, a lexicographic goal programming (LGP) method is proposed to determine local weights from inconsistent interval judgement matrices. Some advantages of LGP are also pointed out.