An integrated approach for deriving priorities in analytic network process

A multiple objective programming approach for the analytic network process (ANP) is proposed to obtain all local priorities for crisp or interval judgments at one time, even in an inconsistent situation. The weakness of the ANP and fuzzy ANP (FANP) is that the complexity of generating priorities is equal to the number of comparison matrices. In the proposed approach, all sets of crisp priorities for each pairwise comparison matrix can be obtained directly. Moreover, from the outcomes of three examples, the power to reach a limiting supermatrix is less than or equal to the power of the FANP. Thus, the proposed approach can be regarded as an efficient alternative of the fuzzy ANP.