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

Area of Science:

• Operations Research
• Decision Science

Background:

• The Ordinal Priority Approach (OPA), introduced in 2020, is a multi-attribute decision-making method utilizing linear programming.
• OPA has gained traction in recent years due to its applicability to real-world decision problems.

Purpose of the Study:

• To propose and analyze two new forms of the OPA: one with strict ordinal relations (OPA-S) and another with weak ordinal relations (OPA-W).
• To deepen the understanding of the mathematical underpinnings of the original OPA.
• To introduce a unified model capable of handling both strict and weak ordinal relations simultaneously.

Main Methods:

• Development of two novel formulations of the OPA: OPA-S and OPA-W.
• Mathematical analysis to compare the proposed forms with the original OPA.
• Application of the developed models to a consumer decision-making problem.

Main Results:

• Demonstration that one of the proposed forms is mathematically equivalent to the original OPA.
• Proof that the original OPA inherently operates under strict ordinal relations.
• Identification of novel mathematical properties of the OPA.
• Successful application of both OPA-S and OPA-W in a practical consumer modeling scenario.

Conclusions:

• The Ordinal Priority Approach is fundamentally a strict ordinal method.
• The proposed OPA-S and OPA-W provide valuable extensions for analyzing decision-making problems with varying degrees of preference information.
• The unified model offers a flexible framework for complex decision scenarios.