CCSD (Correlation Coefficient and Standard Deviation)

CCSD is not a ranking method; it does not rank alternatives, it produces criterion weights from the decision table itself. These weights then become the input to a ranking method such as TOPSIS, VIKOR or SAW. CCSD inherits CRITIC's logic: a criterion receives more weight if it both discriminates strongly between alternatives and says something different from what the other criteria say. But it follows a different route from CRITIC: it measures the relationship between criteria not through pairwise correlations, but through each criterion's contribution to the "overall evaluation" (the weighted sum of all the other criteria). This means the weights cannot be found with a closed-form formula but must be found by solving a system of equations, because the overall evaluation depends on the weights and the weights depend on the relationship with the overall evaluation. Wang and Luo proposed the method in 2010. The output is a weight vector that sums to 1.

Two ideas lie behind CCSD. The first it shares with CRITIC: the more a criterion separates alternatives from one another, the more information it carries; this is measured by the criterion's standard deviation. The second is specific to CCSD: if a criterion is removed and the weighted sum of the remaining criteria is examined, how similarly does that sum behave to the removed criterion? If removing a criterion barely changes the overall evaluation, that criterion is already represented by the others and receives a low weight. If removing a criterion changes the overall evaluation markedly, that criterion carries information of its own and receives a high weight.

This philosophy has a consequence: because the "overall evaluation" is itself built from the very weights being sought, a criterion's relationship with that evaluation is also indirectly tied to the weights. The method resolves this circularity with a system of equations: it searches for the single point at which the weights are consistent with the overall evaluation they themselves define. This makes CCSD more complex than CRITIC, but conceptually a tighter form of objective weighting.

The method proceeds through four steps.

First, scale equalisation. Every column is scaled to between 0 and 1, using the column's own minimum and maximum, with direction corrected so that the largest value maps to 1 for a "higher is better" criterion and the smallest value maps to 1 for a "lower is better" criterion. This step both removes units and aligns directions.

Second, spread. The standard deviation of the equalised values is computed for every criterion. This measures how much the criterion discriminates between alternatives; it carries the same logic as the spread measure in CRITIC.

Third, relationship with the overall evaluation. For a candidate set of weights, every criterion is removed one at a time, and the weighted sum of the remaining criteria under these candidate weights (the overall evaluation) is computed. The correlation between the removed criterion's own column and this overall evaluation is measured. Because this correlation depends on the candidate weights, this step must be recomputed every time the candidate weights change.

Fourth, solving for the weights. The method requires that, for every criterion, the product of its weight and its "disagreement with the overall evaluation" (the square root of the distance of the correlation from 1) be proportional across all criteria in total. Because this condition is self-referential (the weight depends on a correlation computed with itself), it is solved through non-linear optimisation: a search continues until the sum of squared differences between the candidate weights and the target weights is driven to zero.

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 CCSD weight jointly measures how much a criterion discriminates between alternatives and how much it says something different from the overall evaluation; it does not measure importance in the decision-maker's eyes. A high weight shows that the criterion both has a large spread and carries information independent of what the other criteria say in common. A low weight shows either that the criterion discriminates little between alternatives, or that it repeats information already represented by the other criteria.

The weights are tightly bound to the table: adding or removing an alternative changes both the spreads and the correlation structure, and so changes the weights the optimisation finds. This dependency also exists in CRITIC, but because CCSD's solution is non-linear, a small change in the data can shift the weights in a less predictable way than in CRITIC.

Thus instead of writing:

"The CCSD analysis proved this criterion is the most important criterion"

the report should read:

"Within this set of alternatives, this criterion is the one that both discriminates most and carries the information most independent of the overall evaluation; the weight reflects this information contribution, not the decision-maker's priority"

CCSD works with crisp data, with a single number in every cell. DecisionMind holds no extension of this method; the base objective weighting method is used on its own.

You need: alternatives in the rows, criteria in the columns, a number in every cell, and no empty cells. You need "higher is better or lower is better" information for every criterion, because scale equalisation is carried out according to this direction. No weights are entered; the method produces the weights. At least two alternatives and two criteria are required; for the correlation and optimisation to work meaningfully, more than five alternatives is recommended. If a criterion is identical across all alternatives, its spread is zero and its weight also comes out zero; that criterion can safely be excluded.

CCSD is a suitable choice where no expert opinion exists or is wanted, where the criterion list contains repeating indicators, and where a tighter measure of "consistency with the overall evaluation" is wanted than CRITIC's pairwise-correlation logic offers. It works, much like CRITIC, in large tables where some criteria, such as financial ratios or environmental indicators, repeat one another.

There are three situations where it should not be used. If the number of alternatives is very small, correlation and optimisation can produce unreliable results. Where the decision-maker explicitly treats one criterion as a priority, CCSD cannot see this, because it looks only at the data. If computational transparency matters and a non-linear optimisation step is hard to explain to the report's reader, the closed-form CRITIC or Entropy may be preferable.

A long list of repeating indicators, and enough alternatives → CCSD

Same need, but a closed-form, more simply explained method is wanted → CRITIC, Entropy

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

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

Fewer than five alternatives → read the CCSD weights with caution, or move to a closed-form objective method

CCSD's most important advantage is that it measures a criterion's contribution not only through pairwise relationships but through how much the overall evaluation changes once that criterion is removed; this can be considered a more holistic "sufficiency test" than CRITIC's pairwise-correlation approach. The method is objective, and the same table gives everyone the same weight. As Ulutaş and colleagues (2020) demonstrate, CCSD can be used and compared alongside other objective or subjective weighting methods; this is a useful feature for testing the robustness of results.

Its limitations follow from this same structure. First, because the weights are the solution of a non-linear system of equations, they are not as transparent as CRITIC's closed-form formula; the intermediate steps are harder to explain to a report's reader. Second, correlation is unreliable with few alternatives; in small tables both spread and correlation can swing to extremes. Third, "information contribution" and "importance" are not the same thing; the decision-maker's values do not show up in the result, a limitation shared by objective weighting methods in general (Zavadskas and Podvezko, 2016). Fourth, the weights are tightly bound to the set of alternatives and the criterion list; adding an alternative means the whole optimisation must be re-solved and the weights rebuilt.

The most common mistake is running CCSD on the raw table; criteria with large units overwhelm the spread measure and the weights come out unit-dependent. The method is defined on the scaled table.

A second mistake is marking a criterion's direction wrongly; if a "lower is better" criterion is marked "higher is better," the scaling direction is reversed and the optimisation locks onto the wrong target. A third mistake is trusting without limit the weights that come out of a table with only three or four alternatives; with few alternatives, correlation and optimisation can be unstable. A fourth mistake is interpreting a criterion that receives a low weight as "unimportant"; a low weight usually means "already consistent with the overall evaluation, that is, repetitive." A fifth mistake is using the weights without checking whether the optimisation converged, that is, whether the objective function genuinely reached zero.

The governing principle is this:

The CCSD weight jointly measures a criterion's spread and its independence from the overall evaluation; a low weight means not "unimportant" but "repeats information already present in the table," and the report must state it that way, and must also confirm that the optimisation converged to zero.