TOPSIS-RAD: Ranking According to Desires

Traditional decision-making methods often rely on the data itself to define the "best" and "worst" possible outcomes. However, this approach can lead to rankings that are skewed by outliers or that fail to align with what a decision-maker actually wants. TOPSIS-RAD: Ranking According to Desires introduces a new framework that replaces these data-driven extremes with explicit, user-defined goals, ensuring that rankings remain stable and relevant to specific requirements.

The Problem with Traditional Ranking

The standard TOPSIS method identifies a Positive Ideal Solution (PIS) and a Negative Ideal Solution (NIS) based on the highest and lowest values present in the current dataset. This creates two primary issues: first, if the dataset contains extreme outliers, the entire ranking can be distorted. Second, it is prone to "rank reversal," where the addition or removal of an irrelevant alternative changes the relative order of the remaining options. Because the "ideal" is defined by the data rather than the user, the results may not reflect the actual needs or aspirations of the decision-maker.

Introducing Vetoed and Desired Performance Levels

TOPSIS-RAD solves these issues by introducing two specific arrays that allow decision-makers to set boundaries before the ranking process begins:

• Vetoed Performance Levels (VPL): This mechanism allows the user to identify and exclude non-viable alternatives before any normalization occurs. By removing these options early, the method prevents them from influencing the ranking frontiers or distorting the final results.

• Desired Performance Levels (DPL): Instead of letting the best-performing data point define the "ideal," the user sets a specific target. Any performance above this level is capped at the DPL. This anchors the Positive Ideal Solution in the user’s actual aspirations, ensuring that performances significantly better than the goal do not disproportionately sway the ranking.

Stability Through User-Defined Boundaries

By grounding the ranking in these fixed, user-specified boundaries, TOPSIS-RAD preserves the familiar distance-based structure of traditional TOPSIS while significantly increasing its reliability. The authors demonstrate these mechanisms through three toy examples, showing how VPL effectively reshapes the boundaries of the analysis and how DPL provides a stable, consistent framework that limits the influence of extreme data points.

Considerations for Implementation

While TOPSIS-RAD offers a more controlled approach to decision-making, it is important to note that the method requires the decision-maker to define these levels explicitly. The authors have provided a "Visual TOPSIS RAD" application to assist with the numerical computations and to help users manage their data templates. As with any decision-support tool, the effectiveness of the ranking depends on the accuracy and appropriateness of the levels set by the user. The paper also includes a discussion on the limitations of this approach and suggests directions for future research.