The Least Penalty Optimization Prioritization Operators for the Analytic Hierarchy Process: A Revised Case of Medical Decision Problem of Organ Transplantation

The Analytic Hierarchy Process (AHP) is one of the popular methods to support human decision making. Prioritization method leading to the possibility of rank reversal is still one of the unsettled issues of the AHP, although many applications of this method have been made. In this study, 10 important prioritization methods are reviewed and compared. To evaluate the fitness of the prioritization operators (POs), on the basis of existing PO measurement criteria, this research proposes the Root Mean Penalty Weighted Square Variance (RMPWSV) as a reasonable measurement criterion. Graphical solution demonstrates the computational concept for the RMPWSV. On the basis of the RMPWSV, two Least Penalty Optimization (LPO) POs are proposed as the new perspectives for solving the prioritization problems: Least Product of Penalty and Direct Squares (LPPDS) and Least Product of Penalty and Weighted Squares (LPPWS). The comprehensive numerical analyses verify that LPPDS is the fittest PO with respect to the RMPWSV. To demonstrate improvement of the proposed method, a medical decision problem for organ transplantation is revised by using 11 developed POs and two proposed POs with respect to RMPWSV measurement. LPPDS is the ideal PO, instead of Eigenvector method, to generate a priority vector for a decision problem in various fields, such as social science, politics, business, finance, medical treatment, resource management, and engineering management.