One of the interesting issues in analytic hierarchy process (AHP) is the consistency of the comparison matrix. The matrix which represents the opinion of decision maker must satisfy the rate of consistency. An inconsistent comparison matrix cannot be used as a reference to make decision. To repair an inconsistent comparison matrix, two objectives should be minimize, namely the consistent ratio of a modified matrix and the deviation between the original and the modified matrix. However, there will be a conflict if both of them are optimized together when repairing the inconsistent matrices. This thesis thus proposes some methods with swarm intelligence to solve the multi-objective problem. The proposed methods are motivated by two well-known algorithms, ant colony optimization (ACO) and particle swarm optimization (PSO), to solve the optimization problem with either single or multi objective. Each proposed method has two types of algorithms to solve the two types of comparison matrices, fuzzy preference matrix (FPM) and multiplicative preference matrix (MPM). They are MOBAF-MOBAM and PSOMOF-PSOMOM. Some examples of inconsistent FPM and MPM are provided to show the performance of the proposed methods. The experimental results demonstrate that the proposed methods produce good alternative solutions that satisfy both objectives when repairing inconsistent matrices. Some solutions are offered in a Pareto graph which shows the consistent ratio of a relation and the deviation matrices. Three metrics are used to measure the performance of the proposed methods. The results show the performance of the proposed methods are better than two other algorithms.

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