Determination of weight vector by using a pairwise comparison matrix based on DEA and Shannon entropy
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Abstract:
The relation between the analytic hierarchy process (AHP) and data envelopment analysis (DEA) is a topic of interest to researchers in this branch of applied mathematics. In this paper, we propose a linear programming model that generates a weight (priority) vector from a pairwise comparison matrix. In this method, which is referred to as the E-DEAHP method, we consider each row of the pairwise comparison matrix as a decision-making unit (DMU). In the normalized pairwise comparison matrix, the arithmetic mean of each row is considered as the output and the entropy of each column as the input of the decision-making unit. The proposed model is capable of producing real weight for a perfectly consistent pairwise comparison matrix. Also, the model does not require that the pairwise comparison matrix has acceptable inconsistency. On the other hand, this model can estimate a robust priority vector for a pairwise comparison matrix. To illustrate the capability of the proposed method, two numerical examples are examined. Also, we analyzed a hierarchical problem in multiple criteria decision making (MCDM) with the proposed model.
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Journal title
volume 8 issue 2
pages 0- 0
publication date 2022-05
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