PAM (Polygons Area Method)

PAM is a method that ranks alternatives through a visual metaphor once you already hold a decision table. Each alternative becomes a polygon plotted on axes spaced at equal angles, one axis per criterion; the distance along each axis reflects the alternative's weighted performance on that criterion. The output is the area of these polygons and a ranking from largest to smallest area; the alternative with the largest area is the best. The method was introduced by Honarmande Azimi and colleagues in 2014, in an application to industrial robot selection.

PAM's underlying idea is to turn a visualisation decision-makers are already familiar with, a spider or radar chart, directly into a score. Each criterion is an axis, each alternative a point on these axes, and the area enclosed by the polygon joining these points is the alternative's overall performance. Because the area rests only on the products of neighbouring axis pairs, being very high on one axis but very low on its neighbours does not inflate the area much. PAM therefore tends to reward alternatives that are good in a balanced way over alternatives that shine on a single axis while staying weak on the others.

The method proceeds through four steps.

First, direction-sensitive transformation. "More is better" criteria are left as they are; "less is better" criteria are inverted, so that the value enters through division rather than multiplication, and a large value always represents "good" on every criterion.

Second, weighted vertex values. Each value is multiplied by its criterion's weight, then each criterion column is rescaled by dividing by its own total. These final values give the polygon's vertex distance, its radius, on that axis.

Third, polygon area. Criteria are placed on a circle at equal angles (360° divided by the number of criteria). Each alternative's polygon area is computed by summing the products of neighbouring axes' vertex distances and scaling by the sine of this angle; this follows naturally from dividing a polygon into triangles formed by neighbouring vertices.

Fourth, ranking. Alternatives are ranked from largest to smallest area; the largest area marks the best alternative.

The formulas behind each step, the intermediate tables and the citation formats are given on the DecisionMind method page; this card carries no formulas.

The polygon area is a relative score produced with this set of alternatives and these weights; it cannot be compared against an area figure from a different analysis, and it does not mean a percentage or a probability. A large area does not mean "best on every criterion"; it reflects the balance between neighbouring axes.

Where there are more than three criteria, a caveat is needed: the polygon's area can depend on the order in which criteria are placed around the circle, because only neighbouring axis pairs are multiplied. In a three-criterion table this order never changes the area, because every axis is already the neighbour of every other axis; with four or more criteria, the axis order must be reported.

Thus instead of writing:

"PAM found the most balanced alternative with certainty"

the report should read:

"With these weights and this alternative set, the alternative with the largest polygon area is this one; where more than four criteria are involved, this result also depends on the order of the axes around the circle"

PAM works with crisp data. DecisionMind holds no extension of this base method.

You need: alternatives in rows, criteria in columns, one number per cell; direction information for every criterion; and criterion weights summing to 1. PAM does not produce weights, it asks for them. In practice a minimum of three criteria is required; with two criteria the polygon's formula mathematically always yields zero area, because the angle between two axes is 180 degrees and the sine of that angle is zero. Three to twelve criteria work comfortably.

PAM is a sound choice if your criteria can be measured numerically, you have at least three of them, and you want to communicate the result to the decision-maker through a visual polygon or radar chart. Typical territory includes multi-criteria comparisons such as equipment, material and supplier selection.

It should not be used where the number of criteria is limited to two, or where you do not want an arbitrary choice of axis order to affect the result. Where criteria are strongly linked, that link needs handling first, because PAM treats criteria as independent axes.

A numerical table, at least three criteria, a wish to communicate the result through a visual polygon → PAM

A two-criterion comparison → TOPSIS, SAW or another direct distance/sum method instead of PAM

No compromise allowed on one criterion, sub-threshold alternatives must be screened out → screening first, then ranking

Weights are needed, not a ranking → AHP, BWM, SWARA (subjective); Entropy, CRITIC (objective)

PAM's greatest strength is its visual explicability. The result maps directly onto a spider-web chart the decision-maker already knows, and which axis each alternative is strong or weak on can be seen at a glance. The computational burden is light, and because the area rests only on neighbouring-axis products, the structure rewards balanced performance.

Its limitations stem from its geometric structure. First, with four or more criteria, the polygon's area can depend on the order in which criteria are placed around the circle; the same data with a different axis order can produce a different area, because only neighbouring axis pairs are multiplied and distant axes are never compared directly. Second, in two-criterion tables the method mathematically always yields zero area, and discriminating power is lost entirely. Third, its literature is very limited; the method has been introduced through a single application paper and does not yet carry the broad body of critique and comparison that methods such as TOPSIS or VIKOR have accumulated (Honarmande Azimi et al., 2014).

The most common mistake is running PAM with two criteria and treating the near-zero areas that result as meaningful; the method is structurally non-discriminating in this case, and a minimum of three criteria is required.

A second mistake is leaving the axis order arbitrary with four or more criteria and treating the result as reproducible; if the axis order changes, the area can change too, and this order should be stated in the report. A third mistake is presenting the polygon area as a percentage or an absolute performance measure; the area is meaningful only with this particular alternative set and these weights.

The governing principle is this:

A PAM result is a product of the chosen weights, and, where there are more than four criteria, of the axis order; if these choices are not stated explicitly in the report, the result is presented incompletely.