PAM - Polygons Area Method

Overview

Apply F.steps in order; final score determines descending ranking.

Output

utility, higher is better

Data

Crisp, complete numeric matrix

Weights

Needs a weight source

Size

2+ alternatives, 3-12 criteria works best

Used for

Alternative selection, Supplier evaluation

How it works

1. 1

   Normalise matrix per criterion (direction-aware to [0,1]).

   $$r_{ij}=\{\begin{array}{ll}(x_{ij}-\min )/(\max -\min )& j\in J^{+}\\ (\max -x_{ij})/(\max -\min )& j\in J^{-}\end{array}$$

   PAM literature, Eq.(1)

2. 2

   Weighted normalised polygon vertices p_ij = w_j · r_ij per criterion.

   $$p_{ij}=w_j{r}_{ij}$$

   PAM literature, Eq.(2)

3. 3

   Polygon area for each alternative (radii arranged on n equal-angle axes 2π/n).

   $${\text{Area}}_i=\frac{1}{2}\sin \left(\frac{2\pi }{n}\right)\sum _{j=1}^n{p}_{ij}{p}_{i,j+1},p_{i,n+1}=p_{i1}$$

   PAM literature, Eq.(3)

4. 4

   Descending ranking by polygon area.

   $$\text{rank}(i)\propto -{\text{Area}}_i$$

   PAM literature, Sec.4

Look elsewhere when

Assumptions to verify

• Criteria preferences are independent (no synergistic interactions)
• Compensation is acceptable: high score on one criterion can offset low on another
• Decision matrix is complete (no missing values)

Edge cases and pitfalls

• Applying PAM without verifying this assumption.

  Requirement: Criteria preferences are independent (no synergistic interactions)

• Applying PAM without verifying this assumption.

  Requirement: Compensation is acceptable: high score on one criterion can offset low on another

• Applying PAM without verifying this assumption.

  Requirement: Decision matrix is complete (no missing values)

• Using PAM when: Criteria strongly correlated → consider DEMATEL/ANP for interdependence.

  An alternative method is recommended in this situation.

• Using PAM when: Non-compensatory preferences → consider outranking (ELECTRE/PROMETHEE).

  An alternative method is recommended in this situation.

Works with

How to cite