CRITIC (CRiteria Importance Through Intercriteria Correlation)

CRITIC is not a ranking method; it does not rank alternatives, it produces criterion weights. Looking at the decision table, it assigns every criterion a weight, with the weights summing to 1. These weights then feed into a ranking method such as TOPSIS, VIKOR or SAW. Like entropy, CRITIC is an objective weighting method, but it rests on two measures at once rather than one: a criterion's own spread and its relationship with the other criteria form these two measures. Diakoulaki, Mavrotas and Papayannakis proposed the method in 1995. The name itself says as much: a criterion's importance arises from its correlation with the other criteria.

Two ideas sit behind CRITIC. The first it shares with entropy: the more a criterion separates the alternatives from one another, the more information it carries. The second is CRITIC's own: if two criteria rise and fall together across every alternative, they are saying the same thing twice. Such a pair injects the same information into the decision twice and gives it double weight in the process. CRITIC penalises this repetition: the less a criterion correlates with the others, the more "distinctive" the information it adds to the table, the more weight it receives.

The consequence of this philosophy is that the weight measures "information contribution", not "importance". A criterion the decision-maker regards as the most important receives a low weight in CRITIC if it correlates almost perfectly with another criterion, because that information is already present in the table. This is exactly what is wanted when the criterion list is long and full of indicators that repeat one another. In small tables where the criteria have been deliberately chosen to complement one another, CRITIC can instead surprise the decision-maker.

The method proceeds through five steps.

First, scale equalisation. Every column is scaled to between 0 and 1 using its own minimum and maximum. For a "higher is better" criterion the largest value becomes 1 and the smallest becomes 0; for a "lower is better" criterion this is reversed, so the smallest value becomes 1. This step both removes units and aligns directions; the next two measures are computed on this equalised table. Computed on the raw table instead, a criterion with large units (currency) would swamp the spread measure.

Second, spread. For every criterion, the standard deviation of the equalised values is computed: this comes out small when values sit close together and large when they are spread apart. This is the measure of how much the criterion discriminates between alternatives.

Third, relationship. A correlation is computed for every pair of criteria: do the two criteria move together across the alternatives, move oppositely, or show no relation. A correlation close to 1 means the two criteria carry the same information.

Fourth, amount of information. For every criterion, the spread is multiplied by the sum of its "conflict" with the other criteria; conflict is the distance of the correlation from 1. A criterion with a large spread and little relationship to the others carries the most information.

Fifth, weight. Every criterion's amount of information is divided by the total information; the result is a weight vector summing to 1. DecisionMind fixes the scale-equalisation and standard-deviation form to the method's definition and states this in the report.

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

A CRITIC weight measures the share of "distinctive information" a criterion contributes to the decision table; it does not measure the importance the decision-maker sees in it. A weight of 0.50 does not mean "this criterion is half of the decision"; it means "half of the independent information in this table comes from this criterion". Two things determine the weight at once: the criterion's spread and its relationship with the other criteria. A criterion with a high spread that moves almost identically with another criterion can still receive a low weight; this is not an error, it is the penalty for repetition.

The weights depend on the table: when the alternative set or the criterion list changes, both the spreads and the correlations change, and the weights are rebuilt. When the number of alternatives is small, correlation is unreliable; a correlation computed from three alternatives tends towards either 1 or minus 1 and drags the weights to the extremes. In small tables, CRITIC weights should be read with caution.

Thus instead of writing:

"The CRITIC analysis revealed that revenue is the most important indicator"

the report should read:

"Within this alternative set, revenue is the indicator that both diverges most and overlaps least with the other indicators; the weight of 0.50 reflects this information contribution, not the decision-maker's order of priority"

Classical CRITIC works with crisp data, meaning a single number in every cell. Unlike entropy, it has no trouble with zero or negative values, because it uses minimum-maximum scaling. But if a criterion is identical across every alternative, its spread comes out at zero and so does its weight; such criteria should be removed beforehand. Alongside the base method, DecisionMind holds fuzzy and spherical fuzzy Z-number extensions, three members in total.

You need: alternatives in rows, criteria in columns, one number per cell, and no empty cells. You also need, for every criterion, whether higher or lower is better, because scale equalisation is carried out according to this direction; a wrong direction reverses the sign of the correlations. Weights are not entered; the method produces them. A minimum of two alternatives and two criteria is required; for the correlation to be meaningful, the number of alternatives should exceed five.

CRITIC is in the right place when the criterion list is long and some of the indicators repeat one another. Financial ratios, sustainability indices, and country or company comparisons are typical examples. CRITIC suppresses this repetition on its own and spares the decision-maker the question of "which indicators are saying the same thing". Where no expert opinion exists or none is wanted, CRITIC is an objective source of weights; where the number of alternatives is large enough, it draws on richer information than entropy.

The situations where it should not be used follow from its own philosophy. If the number of alternatives is very small, correlation is unreliable and the weights run to the extremes. If the criteria were already chosen to be independent of one another, the second measure adds nothing and the method behaves like entropy. Where the decision-maker clearly regards one criterion as a priority, CRITIC cannot see this. Criteria being related to one another can itself be a deliberate choice by the decision-maker; the same dimension may deliberately be measured from several angles. In such cases, CRITIC's penalty for repetition produces an unwanted result.

A long, repetitive indicator list, sufficient alternatives → CRITIC

Only spread matters, criteria are independent → Entropy

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

Both preference and data matter → a combination of subjective and objective weights

Fewer than five alternatives → read CRITIC's weights with caution or switch to a subjective method

CRITIC's most important strength is that it suppresses repetitive criteria on its own. Long indicator lists often hold three or four indicators measuring the same phenomenon; conventional weighting would count that phenomenon three or four times over, whereas CRITIC counts it once. CRITIC is objective: the same table gives everyone the same weights. Because it clears away directions and units through scale equalisation, it is unaffected by scale differences in the raw data. Its calculation is transparent; the spread and correlation tables can be shown in the report and give a visible answer to "which criteria overlap".

Its limitations stem from the same structure. First, correlation is unreliable with few alternatives; in small tables the weights run to the extremes, and a single alternative's value can flip the sign of the correlation. Second, correlation measures a linear relationship; if two criteria are related in a non-linear way, the repetition goes unseen. Third, "information contribution" and "importance" are not the same thing; the decision-maker's values do not show up in the result. Fourth, the weights depend on the alternative set and the criterion list; adding one criterion changes the entire correlation structure and, with it, every weight. Fifth, a direction error in scale equalisation reverses the sign of the correlation, and this is difficult to notice. Žižović, Miljković and Marinković (2020) discuss and revise the way the product of standard deviation and correlation is turned into a weight; for a comparison of objective methods, see Zavadskas and Podvezko (2016).

The most common mistake is running CRITIC on the raw table; a criterion with large units swamps the spread measure and the weights come out dependent on units. The method is defined on the equalised table.

A second mistake is marking the criterion direction wrongly; if a "lower is better" criterion is marked "higher is better", the sign of the correlations flips and the repetition penalty falls on the wrong criterion. A third mistake is trusting weights derived from a table of three or four alternatives. A fourth mistake is interpreting a criterion with a low weight as "unimportant"; a low weight usually means "this overlaps with another criterion". A fifth is leaving a constant criterion in the table; its weight comes out at zero. A sixth is using one study's CRITIC weights on a different alternative set.

The governing principle is this:

A CRITIC weight measures two things together, spread and distinctiveness; a low weight does not mean "unimportant" but "repeats information already present in the table", and the report must say so.