Backpropagation multi-layer perceptron for incomplete pairwise comparison matrices in analytic hierarchy process

Analytic hierarchy process (AHP) is a widely used decision making method in many areas such as management sciences. The performance ratings of multiple criteria and alternatives can be elicited from pairwise comparisons obtained by expressing the decision maker’s perceive. However, it may be difficult for the decision maker to prudently assign values to comparisons for large number of criteria or alternatives. Since there exist distinct relationships between any two elements in the real world, the relationship between the missing comparison and the assigned comparisons should be taken into account. The aim of this paper is to propose a novel method using a well-known regression tool, namely the backpropagation multi-layer perceptron (i.e., MLP) to realize the above implicit relationship so as to estimate a missing pairwise judgment from the other assigned entries. A computer simulation is employed to demonstrate that the proposed method can effectively find a missing entry of an incomplete pairwise matrix such that its consistency index is minimized.