A cosine maximization method for the priority vector derivation in AHP

作者：Kou, Gang^*; Lin, Changsheng

来源：European Journal of Operational Research, 2014, 235(1): 225-232.

DOI：10.1016/j.ejor.2013.10.019

• Analytic Hierarchy Process
• Pair-wise comparison matrix
• Cosine similarity measure
• Priority vector
• Consistency index

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.

• 出版日期2014-5-16
• 单位长江师范学院; 电子科技大学; 西南财经大学