A cosine maximization method for the priority vector derivation in AHP

By Gang Kou, Changsheng Lin. European Journal of Operational Research, 2014

318 citations recorded by the source corpus.

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.

Subfields: Ecological Modeling, Management Science and Operations Research, Safety, Risk, Reliability and Quality

View Paper: https://www.semanticscholar.org/paper/9254c52a6901110065eeb5bde3197ffedd5d45c1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Management Science and Operations Research

1. Xin Ma
2. Sheng-Li Si
3. Ping Zhang
4. Xiao-Yue You
5. Hu-chen Liu
6. William Ho
7. Alessio Ishizaka
8. Ashraf Labib

In Safety, Risk, Reliability and Quality

1. Hu-chen Liu
2. William Ho

Citations in the corpus

• DEMATEL Technique: A Systematic Review of the State-of-the-Art Literature on Methodologies and Applications (2018, background): “In the AHP, a hierarchy considers the distribution of a goal among the elements being compared and judges which element has a greater influence on that goal [33, 34].”
• The state-of-the-art integrations and applications of the analytic hierarchy process (2017, background): “, 2014), and modifying the priority vector derivation (Kou and Lin, 2014), do not meet the criteria because they lack of real-world applications.”