Dissertation (MSc Mathematics)This dissertation centers on comparing two methods based on consistence and ranking preservation of alternatives in analytic hierarchy process (AHP) by using the best job example. These two methods logarithmic least square method (LLSM) and eigenvalue method (EM) are used to develop approximations of ratio scales from a positive reciprocal matrix. The measurement of consistency and rank preservation are the main criteria for comparison of these two methods. The priorities obtained for each method from the combination of the comparison matrices for all criteria with respect to all alternatives, the ranking of the alternatives were given against the four covering criteria, the results show that, the two methods namely LLSM and EM give different results on ranking the alternatives as shown by Saaty and Vargas(1984).