A cosine maximization method for the priority vector derivation in AHP

Gang Kou and Changsheng Lin

European Journal of Operational Research, 2014, vol. 235, issue 1, 225-232

Abstract: The derivation of a priority vector from a pair-wise comparison matrix (PCM) is an important issue in the Analytic Hierarchy Process (AHP). The existing methods for the priority vector derivation from PCM include eigenvector method (EV), weighted least squares method (WLS), additive normalization method (AN), logarithmic least squares method (LLS), etc. The derived priority vector should be as similar to each column vector of the PCM as possible if a pair-wise comparison matrix (PCM) is not perfectly consistent. Therefore, a cosine maximization method (CM) based on similarity measure is proposed, which maximizes the sum of the cosine of the angle between the priority vector and each column vector of a PCM. An optimization model for the CM is proposed to derive the reliable priority vector. Using three numerical examples, the CM is compared with the other prioritization methods based on two performance evaluation criteria: Euclidean distance and minimum violation. The results show that the CM is flexible and efficient.

Keywords: Analytic Hierarchy Process; Pair-wise comparison matrix; Cosine similarity measure; Priority vector; Consistency index (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (100)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:235:y:2014:i:1:p:225-232

DOI: 10.1016/j.ejor.2013.10.019

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