VIKOR (VlseKriterijumska Optimizacija I Kompromisno Resenje)

VIKOR is a compromise-ranking method that starts from a decision table filled with numbers. Its name abbreviates the Serbian phrase for "multicriteria optimisation and compromise solution." Its output is three values for every alternative: group utility (S), individual regret (R) and a compromise index (Q) that combines the two. Alternatives are ranked by Q, and a lower Q is better. What sets the method apart from other ranking techniques is that it delivers the result not merely as a ranking but as a "compromise solution" or "compromise set" tested against two conditions. Serafim Opricovic developed it in 1998 for civil-engineering systems, and it gained currency through Opricovic and Tzeng's 2004 paper comparing it with TOPSIS. It does not generate criterion weights; weights come from outside.

VIKOR's underlying question is not "which alternative is best" but "which alternative wins the widest acceptance." An alternative can be very good overall yet poor on a single criterion, and whoever cares about that criterion will object to it. The method makes this tension visible through two separate measures: group utility is the alternative's total distance from the ideal across all criteria and stands for "the benefit of the majority"; individual regret is the alternative's distance on the single criterion where it fares worst and stands for "the objection of the worst-off party." The compromise solution is the balance point between the two: the alternative that gives the majority the greatest benefit while keeping the minority's regret smallest.

This philosophy has two consequences. First, VIKOR is compensatory, though less so than TOPSIS: the individual-regret measure partly stops a severe weakness on one criterion from dissolving into the total. Second, VIKOR avoids declaring a single winner; if the top-ranked alternative is not sufficiently separated from the second, or is not best on both the total and the single worst criterion, the method proposes several alternatives together as a compromise set. This is a philosophy built for settings where the decision rests on a discussion rather than a single figure.

The method proceeds through four steps.

First, the best and worst value of each criterion. VIKOR identifies the best value (largest for a benefit, smallest for a cost) and the worst value for every column in the table. Unlike TOPSIS, it does not construct a hypothetical ideal alternative; it simply holds on to the two extreme values.

Second, group utility and individual regret. VIKOR takes each alternative's distance from the ideal on every criterion and divides it by the range between that criterion's best and worst value, bringing it between 0 and 1; this is called linear normalisation and is VIKOR's route to scale equalisation (unlike TOPSIS's vector normalisation, it divides by the gap between best and worst rather than by the column's magnitude). VIKOR multiplies these distances by the criterion weights. The sum of the weighted distances is the group utility S: a small S says the alternative is close to the ideal across all criteria. The largest of the weighted distances is the individual regret R: a small R says the alternative is not badly off on any single criterion.

Third, the compromise index. VIKOR brings S and R onto their own 0–1 scales and combines them with a coefficient. This coefficient (v) answers the question "how much weight should go to the majority's benefit versus the minority's regret": 0.5 weights the two equally, values above 0.5 favour group utility, and values below it favour individual regret. The result is the Q index, where a lower Q is better. In DecisionMind, v defaults to 0.5 and the user can change it between 0 and 1.

Fourth, two conditions. The alternative with the smallest Q is the candidate compromise solution, but it must pass two conditions. Acceptable advantage: the Q gap to the second-ranked alternative must be large enough; the threshold depends on the number of alternatives and grows as that number falls (0.5 for three alternatives, 0.25 for five). Acceptable stability: the candidate must also rank first by S or by R, so that its lead does not come from the combining coefficient alone. If both conditions hold, there is a single compromise solution. If the stability condition fails, the first two alternatives are proposed together. If the advantage condition fails, every alternative whose Q gap falls below the threshold is proposed as a compromise set.

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

VIKOR's output is three columns, read together. The S column answers "how far is this alternative from the ideal overall," the R column answers "how bad is this alternative's worst criterion," and the Q column answers the balance between the two. A lower value is better; the best alternative's Q is 0, the worst's is 1. A Q of 0 does not mean "flawless" but "best in this set on both the total and the worst criterion."

The real result is not the Q ranking but the verdict the two conditions produce. "The single compromise solution is A2" and "the compromise set is A2 and A1" are different outcomes, and the second is not a weakness but the method's honesty: if the data does not separate two alternatives enough, the method says so. Reporting only the alternative with the smallest Q is therefore a misuse of VIKOR. Reading S and R separately also carries information: an alternative that ranks first on S but last on R is good overall yet troubles everyone on one criterion, and the decision-maker should see this.

Thus instead of writing:

"VIKOR shows A2 as the best alternative"

the report should read:

"With these weights and v = 0.5, A2 is the single compromise solution; it ranks first on both group utility and individual regret, and its gap to the second alternative exceeds the acceptance threshold"

and if either condition fails, the compromise set is stated as such.

Classical VIKOR works with crisp data: one number per cell. If your data is approximate, given as a range, or contradictory across experts, the data type changes: VIKOR has fuzzy, grey, intuitionistic, neutrosophic, linguistic and other extensions, and DecisionMind holds twenty-four VIKOR members alongside the base method, seven of them fuzzy extensions. Which extension fits which data situation is explained on the relevant data-type cards; the tool asks about your data type and suggests the right member.

You need alternatives in rows, criteria in columns, one number per cell and no empty cells; for every criterion, whether more is better or less is better; criterion weights that sum to 1; and a decision on the compromise coefficient v (default 0.5). VIKOR does not produce weights, it asks for them; weights are derived from expert opinion (AHP, BWM, SWARA) or from the data itself (Entropy, CRITIC). A minimum of two alternatives and two criteria is required, and three to twelve criteria work comfortably. When the number of alternatives is small, the advantage threshold grows and finding a single solution becomes harder; this is not a flaw but the price of not speaking with certainty on a small set of alternatives.

VIKOR is a sound choice if your criteria can be measured numerically, the interests of several parties conflict, and you are looking for the alternative that draws the least objection rather than the outright best. Its typical territory includes engineering design, facility and site selection, prioritising public investment, and any decision that needs agreement among stakeholders. It works on the same table as TOPSIS; the difference is that TOPSIS looks only at total distance, while VIKOR separately weighs the worst performance on a single criterion. The same table can receive different rankings from the two methods, and this is not an error but two different decision philosophies.

It should not be used in the following situations: where no compromise at all is acceptable on one criterion (VIKOR limits regret but does not eliminate it; where strict elimination is required, use outranking methods instead), where criteria are strongly linked to one another (VIKOR treats criteria as independent), and where the decision-maker cannot make sense of the S/R distinction and the v coefficient (in that case TOPSIS's single score is easier to follow).

A numerical table, conflicting interests, "least objection" sought → VIKOR

A numerical table, compensation accepted, a single total score suffices → TOPSIS

Same goal, but the data is fuzzy / grey / intuitionistic → the relevant VIKOR extension

No compromise allowed on one criterion, sub-threshold alternatives must be eliminated → outranking methods (ELECTRE, PROMETHEE)

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

VIKOR's greatest strength is that it delivers its result conditionally: when alternatives are not sufficiently separated, it does not declare a single winner but offers a compromise set. This is both more honest and more useful for the decision-maker, since a short list emerges on its own. Its second strength is keeping the "worst criterion" measure separate: an alternative with a serious weakness on a single criterion stays visible with that weakness even if it is good overall. Third, because linear normalisation is anchored to the best and worst values, the result can be read as "how much of what is possible in this set has been achieved." The computational burden is small, and the steps can be followed on the table.

First, the compromise coefficient v is a decision that affects the result; chosen without justification, the ranking is equally unjustified. Opricovic and Tzeng (2007) show that at its extreme values the method reduces to pure group utility or pure individual regret; compromise exists only at the values in between. Second, when the alternative set changes, the best and worst values shift, so an alternative added later can change the order of the others (rank reversal; Opricovic and Tzeng, 2007). Third, although not full compensation, compensation is still present: the regret measure makes a weakness visible but does not eliminate it. Fourth, the two conditions are sensitive to the number of alternatives; finding a single solution with only two or three alternatives is difficult, and the result is often a set. Fifth, the assumption that criteria are independent and the fact that weights come from outside are limits shared with TOPSIS.

The most common mistake is skipping the two conditions and reporting only the smallest-Q alternative as the "winner"; VIKOR's defining feature is the compromise set, not a single winner. A second mistake is reversing the best and worst value for cost criteria: for a cost criterion the best value is the smallest, and reversing this makes the expensive alternative count as ideal. A third mistake is setting the v coefficient to 0 or 1, at which point the method stops being a compromise method. A fourth is choosing v without justification and not stating this in the report. A fifth is dropping the S and R columns and showing only Q; the decision-maker needs to see why an alternative creates regret. A sixth is reading a different ranking from VIKOR and TOPSIS on the same table as meaning "one of them is wrong."

The governing principle is this:

VIKOR's result is not a ranking but a conditional compromise proposal; VIKOR has not been properly applied unless the v coefficient, the S and R columns, and the outcome of the two conditions are given together in the report.