Strict and weak ordinal relations for estimating the criteria weights in Ordinal Priority Approach (OPA)

The Ordinal Priority Approach (OPA) is a recent multiple attribute decision-making that was published in 2020. This method uses a linear programming approach to solve decision-making problems in real-life situations. Due to its application in real-world situations, it has been employed by scholars widely in recent years. This study proposes two forms of the OPA for multiple attribute decision-making; one with strict ordinal relations and the other with weak ordinal relations. New forms are crucial in understanding the mathematical theory behind the original OPA. The study shows that one of the proposed forms and the original OPA are two forms of the same model. The study proves that the OPA is strict rather than weak. The study also found some new properties of the OPA. The application of the strict and weak OPA models is presented in a consumer modeling problem.•Revisits the Ordinal Priority Approach (OPA) to Multiple Attribute Decision Making.•Proposes the OPA with Strict Ordinal Relations (OPA-S) and Weak Ordinal Relations (OPA-W).•Proposes a model to consider both weak and strict ordinal relations at the same time.