Ordinal priority approach

Ordinal priority approach (OPA) is a multiple-criteria decision analysis method that aids in solving the group decision-making problems based on preference relations. Various methods have been proposed to solve multi-criteria decision-making problems. The basis of most methods such as analytic hierarchy process and analytic network process is pairwise comparison matrix. The advantages and disadvantages of the pairwise comparison matrix were discussed by Munier and Hontoria in their book. In recent years, the OPA method was proposed to solve the multi-criteria decision-making problems based on the ordinal data instead of using the pairwise comparison matrix. The OPA method is a major part of Dr. Amin Mahmoudi's PhD thesis from the Southeast University of China. This method uses linear programming approach to compute the weights of experts, criteria, and alternatives simultaneously. The main reason for using ordinal data in the OPA method is the accessibility and accuracy of the ordinal data compared with exact ratios used in group decision-making problems involved with humans. In real-world situations, the experts might not have enough knowledge regarding one alternative or criterion. In this case, the input data of the problem is incomplete, which needs to be incorporated into the linear programming of the OPA. To handle the incomplete input data in the OPA method, the constraints related to the criteria or alternatives should be removed from the OPA linear-programming model. Various types of data normalization methods have been employed in multi-criteria decision-making methods in recent years. Palczewski and Sałabun showed that using various data normalization methods can change the final ranks of the multi-criteria decision-making methods. Javed and colleagues showed that a multiple-criteria decision-making problem can be solved by avoiding the data normalization. There is no need to normalize the preference relations and thus, the OPA method does not require data normalization.