NMD (New Method of Determining Objective Criterion Weights)

Like entropy, CRITIC and LOPCOW, NMD is not a ranking method; it does not rank alternatives, it produces criterion weights. If you hold a numerical decision table of alternatives and criteria, it scans the table without consulting an expert and extracts a weight vector that sums to 1. These weights then feed into a ranking method such as TOPSIS or VIKOR.

Bulut proposed the method in 2017, in a study comparing criterion-weighting methods used for ship propulsion system selection. The name says exactly what it does: "a new way of determining criterion weights." NMD's distinguishing point is that, unlike entropy and CRITIC, it looks not at the spread of the distribution but directly at the column mean.

Entropy, CRITIC and LOPCOW all proceed from a shared idea: the more the alternatives diverge in value on a criterion, the more that criterion determines the decision. NMD departs slightly from this family: rather than how much the alternatives diverge from one another, it looks at how far, on average, they all sit together from the best alternative. In a scaled column, the best alternative always carries the value 1; the closer the column's mean is to 1, the closer the alternatives are, on this criterion, to "good," and NMD judges this criterion to carry little information. The further the mean is from 1, the weaker the alternatives are on average on that criterion, and NMD judges it more discriminating and weights it higher.

A consequence follows: NMD is influenced by the alternatives' general position on a criterion rather than by any single extreme value; this sets it apart from LODECI, which rests on the largest gap, and from entropy, which looks at the evenness of the distribution. Where the question "how far behind are the alternatives on average on this criterion" can be taken as the question that should govern the decision, NMD is in the right place.

The method proceeds through two steps.

First, scale equalisation. In a "higher is better" criterion, every value is divided by the largest value in its column; in a "lower is better" criterion, the smallest value in the column is divided by every value. As a result the best alternative takes the value 1 on every criterion, the others remain below 1.

Second, the weight. Each column's mean is computed and subtracted from one; this difference shows how far, on average, the alternatives on that criterion sit from the best value. These differences are summed across all criteria, and each criterion's own difference is divided by this sum to give its weight.

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

The NMD weight does not measure a criterion's importance in the decision-maker's eyes; it measures how far, on average, the alternatives sit from the best value on that criterion. A weight of 0.41 does not mean "this criterion is 41 per cent of the decision"; it means "the alternatives sit, on average, furthest from the best value on this criterion, and so this criterion is the most discriminating in the decision." If every alternative sits at the best value on a criterion (the mean is exactly 1), that criterion's difference is zero and its weight comes out at zero; this criterion distinguishes nothing in the table.

The weights depend on the alternative set: adding or removing an alternative changes the column mean, and all the weights are rebuilt. Because NMD rests on the mean, it is not as sensitive to a single extreme alternative as LODECI, but with few alternatives (two or three), the mean can still be overly sensitive to a single value.

Therefore, instead of writing:

"The NMD analysis showed that reliability was the most important criterion"

the report should read:

"The alternatives sit, on average, furthest from the best value on the reliability criterion; the NMD weight of 0.41 reflects this distance, not the criterion's priority in the decision-maker's eyes"

Classical NMD works with crisp data: one number per cell. Values must be positive; zero renders the scale-equalisation step undefined for a "lower is better" criterion. DecisionMind does not currently hold an extension of NMD; it stands as a single member.

You need alternatives in rows, criteria in columns, one positive number per cell, and no empty cells. For every criterion, whether more is better or less is better is required, since scale equalisation is done according to this direction. Weights are not entered; the method produces them. A minimum of two alternatives and two criteria is required; as the number of alternatives grows, the mean is computed more stably.

Where there is no expert opinion, or none is wanted, and the decision is thought to be governed by how far, on average, the alternatives sit from the best value on a criterion, NMD is a suitable source of weights. It works meaningfully in situations such as engineering and equipment selection, where the alternatives' technical characteristics are assessed against an ideal reference value.

The cases where it should not be used follow from its philosophy. If the decision is governed not by average distance but by sharp differences between alternatives, LODECI is more suitable; if it is governed by the evenness of the distribution, entropy is more suitable. Where the decision-maker clearly regards one criterion as a priority, NMD cannot see that. If every alternative equals the best value on a criterion, its weight comes out at zero, and that criterion should be removed from the table.

No expert opinion, average distance governs the decision → NMD

The sharpest difference governs the decision → LODECI

The evenness of the distribution governs the decision → Entropy

The decision-maker's priority should show in the result → AHP, BWM, SWARA (subjective)

NMD's most important advantage is its simplicity: the calculation consists only of scaling, taking a mean and normalising, and requires no advanced statistics. It is objective, giving the same table the same weight for anyone. Because it rests on the mean, it is not as sensitive to a single extreme value as LODECI, which makes it more stable on medium-sized tables.

Its limitations stem from the same structure. First, because it rests on the mean, a criterion's true discriminating power (how much the alternatives differ from one another) can be confused with average distance (how far, on average, the alternatives sit from the best); two criteria can share the same mean while one is made of alternatives clustered tightly together and the other of alternatives spread widely apart. Second, the weights depend on the alternative set: adding or removing an alternative changes the mean, and so all the weights. Third, because the method's name is generic, it is hard to search for in the literature, and independent comparison studies are limited; Zavadskas and Podvezko's (2016) assessment of the general limitations of objective weighting methods is also a useful guide here. Fourth, it cannot work directly with zero or negative values.

The most common mistake is reporting the NMD weight as "importance." The weight measures not the criterion's value in the decision-maker's eyes but how far, on average, the alternatives sit from the best value on that criterion.

A second mistake is marking criterion direction wrongly; if a "lower is better" criterion is marked "higher is better," scale equalisation runs backwards and the weight is misdirected. A third mistake is placing excessive trust in a weight drawn from a table of only two or three alternatives. A fourth mistake is using one study's NMD weights on a different alternative set. A fifth is keeping in the table a criterion on which every alternative equals the best value and treating its zero weight as a "method error."

The governing principle is this:

The NMD weight measures how far, on average, the alternatives sit from the best value on a criterion; a high weight does not mean "the criterion is important" but "the alternatives are, on average, weak on this criterion."