EVAMIX (Evaluation of Mixed Data)

Most ranking methods assume every criterion arrives as a numerical measurement. Real decisions are not always like this: an expert panel's "this is better, that is worse" preference ordering, a satisfaction ranking from a survey, or a quality grade (good, average, poor) carries only its order, not the size of the gap between positions. EVAMIX (Evaluation of Mixed Data) is a ranking method that evaluates numerical (cardinal) and ordinal criteria together in the same table, without converting one into the other. Voogd (1983) proposed it for urban and regional planning assessments; its output is a net dominance score for every alternative and a rank based on that score.

Many methods treat ranking information (first, second, third) as if it were a numerical scale; this amounts to inventing information about the size of the gap that does not actually exist. EVAMIX rejects this confusion. For numerical criteria it measures the size of the difference between two alternatives (how many units better); for ordinal criteria it uses only the direction (which is better, not by how much). For every pair of alternatives, a dominance score is first computed from the ordinal criteria and a separate dominance score from the numerical criteria; the two are then reduced to a single dominance score, combined according to the total weight each carries.

This idea has one consequence. EVAMIX is compensatory: a weakness on one criterion can be balanced by strength on another. But this balancing is done by adding up the contribution each measurement type computes in its own way, without mixing the two types (number and rank) together.

The method proceeds through two steps.

First step, two separate dominance calculations. Numerical criteria are first scaled between 0 and 1 according to their direction (for a benefit criterion the smallest value becomes 0 and the largest 1; the reverse for a cost criterion). For every pair of alternatives, cardinal dominance is the weighted sum of the differences between the scaled values. For ordinal criteria, only which alternative leads on that criterion is considered; dominance is the weighted sum of this direction information, carrying only the sign of the difference, not its size.

Second step, combination and ranking. The two dominance scores are combined into a single dominance score, weighted by the total weight of the ordinal criteria and the total weight of the numerical criteria. Each alternative's dominance scores against all other alternatives are summed to give a net score; alternatives are ranked by this net score from highest to lowest.

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 net dominance score shows how much an alternative dominates, or is dominated by, all other alternatives in total; unlike TOPSIS, it does not sit within a fixed 0 to 1 range and can be positive or negative. A positive score shows the alternative is above average, a negative score below average; a score close to zero means the alternative is in the middle of the pack. The size of the score depends on how many alternatives it is compared against and with what weights, so it cannot be compared directly with an EVAMIX score from a different set of alternatives.

Thus instead of writing:

"This alternative has the highest score, so it must be clearly the best"

the report should read:

"For this set of alternatives and these weights, this alternative leads in the combined dominance of the numerical and ordinal criteria; the size of the score is specific only to this comparison"

Crisp data. DecisionMind currently has no extension of this method. You need, for every criterion, a scale type (numerical or ordinal), direction information (higher or lower is better), and weights summing to 1. EVAMIX does not produce weights, it takes them from outside. If all criteria are numerical, the method reduces to a standard pairwise dominance comparison; if all are ordinal, it reduces to a sign-based method (similar to REGIME). At least two alternatives and two criteria are required; the practical range is three to twelve criteria.

If some of your criteria can only be expressed through a ranking or preference order (an expert-panel ranking, a survey satisfaction order, a quality grade) and the rest are numerically measurable, EVAMIX is a way to combine the two without converting one into the other. Its typical fields are urban and regional planning, personnel selection and industrial decision contexts (Darji and Rao, 2013).

There are two situations in which it should not be used. If all your criteria are numerical, EVAMIX adds needless complexity; direct numerical methods such as TOPSIS are sufficient. If all your criteria are ordinal, EVAMIX's numerical side is left idle; methods that work with rank information alone (such as REGIME) are a more direct choice.

Some criteria are numbers, some only ranks → EVAMIX

All criteria are numerical → TOPSIS

All criteria are ranks only → REGIME or similar rank-based methods

No compromise is accepted on one criterion → not EVAMIX; screen first, then rank

EVAMIX's most important strength is that it does not force ordinal data to be treated as if it were numerical; many methods, by not observing this distinction (Hajkowicz and Higgins, 2008), use an ordinal ranking as though it were an equal-interval scale. Because EVAMIX processes each measurement type by its own logic before combining them, it does not claim more information than actually exists in the decision table. Its ability to bring together different measurement types in a single analysis offers a practical solution for the mixed-data situations often met in the field.

Its limitations also stem from its own structure. First, EVAMIX is compensatory: a weakness on one criterion is balanced by strength on another, and this balancing can create a heavy dependence on dominantly weighted criteria (Jeffreys, 2004). Second, because the net dominance score does not sit within a fixed range, it is not read as intuitively as TOPSIS's closeness score; the size of the score is specific to that analysis alone. Third, if all criteria turn out numerical or all ordinal, the method loses its own specific contribution and reduces to simpler methods. Fourth, because only direction is used for ordinal criteria, information about whether the gap between two alternatives is small or large is entirely lost; a very close pair and a very distant pair on an ordinal criterion are processed with the same weight.

The most common mistake is feeding an ordinal criterion (for example, a survey ranking) into the same normalisation as the numerical criteria as though it were an equal-interval scale; preventing exactly this is the whole point of EVAMIX. A second mistake is choosing EVAMIX when all criteria are of the same type (all numerical or all ordinal) and gaining nothing from the method's own specific contribution. A third is reading the net dominance score the way one reads TOPSIS's closeness score, as a percentage between 0 and 1; the EVAMIX score has no such range. A fourth is treating a small and a large difference on ordinal criteria as equally important and never noting this distinction in the report.

The governing principle is this:

An EVAMIX result is a weighted combination of the dominance carried separately by numerical and ordinal information; it must not be forgotten that information on ordinal criteria carries only direction, not size.