CRADIS (Compromise Ranking of Alternatives from Distance to Ideal Solution)

CRADIS is a ranking method for when you already hold a decision table filled with numbers and want the alternatives arranged in a single order. Its output is a compromise score between 0 and 1 for every alternative; the method ranks alternatives by this score. CRADIS produces no weights, taking them from outside. Puška, Stević and Pamučar proposed this method in 2021, in a study on the selection of a healthcare-waste incineration facility. Researchers soon began applying the method to supply chains, green supplier selection and engineering appraisal, and extended it to uncertain data types such as fuzzy sets and Z-numbers.

The idea behind CRADIS is this: use, as TOPSIS does, the logic of "close to the ideal, far from the anti-ideal," but do not combine these two distances into a single Euclidean distance. CRADIS instead calculates two separate utility ratios. The first ratio shows how close you sit to the ideal; it is proportional to the best alternative's distance from the ideal. The second ratio shows how far you sit from the anti-ideal; it is proportional to the worst alternative's distance from the anti-ideal. The average of these two ratios gives the "compromise" score. This is where the method's name comes from.

This idea carries a philosophical consequence. CRADIS carries a compromise-oriented logic close to the VIKOR family. But unlike VIKOR, it does not strike a balance between group utility and individual regret. Instead, it keeps closeness to the ideal and distance from the anti-ideal as two independent, equally weighted ratios, then takes the average of these two ratios. The method is compensatory: a weakness on one criterion can be masked by strength on another.

The method proceeds through five steps.

First, direction-sensitive scale equalisation. For benefit criteria, the method divides every value by the column's largest value. For cost criteria, it divides the column's smallest value by every value. In both directions, a larger number thereby means "good," and every column is compressed into the range 0 to 1.

Second, weighting. The method multiplies every equalised column by its criterion's weight. Weights come from outside CRADIS itself; they must sum to 1.

Third, calculating distance from the ideal and the anti-ideal. In the weighted table, the method treats each column's best value as the ideal and its worst value as the anti-ideal. For every alternative, it calculates how far it falls short of the ideal; this value is the sum of the differences between the ideal and the alternative. It also calculates how far above the anti-ideal every alternative sits; this value is the sum of the differences between the alternative and the anti-ideal.

Fourth, calculating the utility ratios. The method divides the shortfall of the alternative that falls least short of the ideal by each alternative's own shortfall, producing a "closeness to the ideal" ratio. This ratio equals 1 for the best alternative. In the same way, it takes as reference the superiority of the alternative that sits furthest above the anti-ideal, and ratios each alternative's own superiority against this. This ratio also approaches 1 for the best alternative.

Fifth, calculating the compromise score. The method averages the two ratios and ranks alternatives by this score from highest to lowest.

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

The compromise score summarises, together, an alternative's closeness to the ideal and its distance from the anti-ideal, relative to the other alternatives in this analysis. It says nothing more. A score of 1 does not mean "perfect," it means "the best alternative in this set on both ratios." The score is not a percentage and cannot be compared with a score from a different analysis. The reason is this: every analysis builds its ideal and anti-ideal points from its own alternatives.

The two components underlying the score must also be checked separately: the closeness-to-ideal ratio and the distance-from-anti-ideal ratio. If an alternative is strong in only one of them, the average can conceal this imbalance.

For that reason, instead of writing:

"CRADIS found the best alternative"

it is correct to write:

"With these weights, the average of the closeness-to-ideal and distance-from-anti-ideal ratios favours this alternative; the ranking is sensitive to the weight on these criteria"

CRADIS works with crisp data: one number per cell. DecisionMind holds three CRADIS members alongside the base method: classical CRADIS, the spherical fuzzy Z-number extension, and the fuzzy Z-number extension. The relevant data-type cards explain which fits your data situation.

You need the following: alternatives in rows, criteria in columns, one number per cell, and no empty cells; direction information for every criterion; and criterion weights summing to 1. CRADIS does not produce weights, it asks for them; you can derive weights from expert opinion (AHP, BWM, SWARA, CIMAS) or from the data itself (Entropy, CRITIC). A minimum of two alternatives and two criteria is required; CRADIS works comfortably with three to twelve criteria.

CRADIS is a suitable choice if your criteria can be measured numerically, the table is completely filled, you accept compensation, and you also want to see "closeness to the ideal" and "distance from the worst" separately. Its typical territory is alternative selection and supplier appraisal.

The case where it should not be used is, as with TOPSIS, one where you will not compromise on one criterion. CRADIS does not prevent this; you must first screen out sub-threshold alternatives and rank only the remainder with CRADIS. Where criteria are strongly linked to one another, that link needs handling first.

A numerical table, compensation accepted, closeness to the ideal and distance from the anti-ideal wanted separately → CRADIS

Same goal, but a single distance measure is enough → TOPSIS

Not "the best" but "the compromise limiting the greatest regret" → VIKOR

No compromise allowed on one criterion, sub-threshold alternatives must be screened out → screening first, then ranking

Not a ranking but weights are needed → AHP, BWM, SWARA, CIMAS (subjective); Entropy, CRITIC (objective)

CRADIS's most important strength is that it keeps closeness to the ideal and distance from the anti-ideal as two separate ratios, rather than dissolving them into a single distance measure. This makes it easier to see which component is driving the result. Its computational burden is small, and its steps can be followed on the table in a manner similar to TOPSIS. CRADIS brings criteria in different units together in a single table and works with the same simplicity as the number of alternatives grows. Researchers soon extended the method to uncertain data types such as fuzzy sets and Z-numbers, which shows its logic transfers to different data environments (Puška, Božanić, Nedeljković and Janošević, 2022).

Its limitations stem partly from the shared TOPSIS family and partly from its own structure. First, the ideal and anti-ideal points shift when the alternative set changes. The rank reversal risk known from TOPSIS also applies to CRADIS. Second, the method assumes full compensation: a serious weakness on one criterion can be masked by others. Third, classical CRADIS requires crisp data and cannot capture uncertainty in expert judgement. This gap is the reason the fuzzy and Z-number extensions were published shortly after the method was proposed (Puška, Božanić, Nedeljković and Janošević, 2022). Fourth, DecisionMind's own validation test has shown this (see Case 1): the compromise score can be markedly sensitive to weight changes in the middle and lower ranks. A small weight shift can reverse the ranking. Fifth, because the method was proposed in 2021, independent rank-reversal studies have not matured as far as those for TOPSIS or VIKOR.

The most common mistake is marking criterion direction wrongly; in that case the method builds the ideal point from the wrong end, and the ranking is reversed.

A second mistake is reporting only the average without examining the two ratios that make up the compromise score separately. These two ratios are closeness to the ideal and distance from the anti-ideal. If an alternative is strong in only one, this information is lost. A third mistake is assigning weights equally without justification. A fourth is adding an alternative once the analysis is finished and being surprised the ranking shifts. A fifth is reading the compromise score as a percentage or a probability and comparing scores from different analyses. A sixth is accepting the result as final without testing whether a small change in weights could reverse the alternatives in the middle and lower ranks.

The governing principle is this:

A CRADIS result is a summary, in terms of closeness to the ideal and distance from the anti-ideal, of the directions, weights and alternative set you supplied; if any weight is contested, the ranking is contested too, and the report must show this.