CILOS (Criterion Impact LOSs)

CILOS is not a ranking method; it does not order alternatives, it produces criterion weights. Given a numerical decision table of alternatives and criteria, it asks no one "which criterion matters more." It looks at how the alternatives in the table stand relative to one another and assigns each criterion a weight, the whole set summing to 1. These weights then feed into a ranking method such as TOPSIS, VIKOR or SAW.

Zavadskas and Podvezko proposed the method in 2016; the "criterion impact loss" idea that gives it its name also forms half of the IDOCRIW method introduced in the same paper. Like Entropy and CRITIC, CILOS belongs to the objective-weighting family; unlike CRITIC, it looks not at correlation between criteria but at the cost of preferring the best alternative on one of them.

The question behind CILOS is this: had you chosen the alternative that is best on one criterion, how much would you lose on the others? For each criterion, it first finds the alternative that is best on that criterion. It then looks at that same alternative's value on every other criterion and compares it against that other criterion's own best value. Where the loss is large, meaning the alternative that leads on one criterion falls seriously behind on another, that other criterion is the one genuinely driving the decision, because ignoring it costs dearly. Where the loss is small, that criterion is already attainable on nearly every alternative and does not move the decision much.

The consequence of this idea is that CILOS defines "importance" as an opportunity cost. A criterion gains weight not because the decision-maker values it, but because sacrificing it turns out to be expensive. If this distinction is acceptable, CILOS is in the right place; if the weight is meant to reflect the decision-maker's own priorities, a subjective method, or a blend of subjective and objective weighting, is needed instead.

The method proceeds through seven steps.

First, converting cost criteria. CILOS works on a "higher is better" logic throughout. For "lower is better" criteria such as price, every value in the column is divided by the column's smallest value; the cheapest alternative becomes 1, more expensive ones fall below 1, and the column can then be read as "higher is better" like the rest.

Second, turning each column into shares. Every value is divided by its own column's total. Each column then consists of shares that sum to 1, bringing criteria measured in different units (currency, kilometres, points) onto common ground.

Third, building the best profile. For each criterion, the method finds which alternative holds the highest share on it. The shares of these alternatives across all criteria are arranged side by side into a table with as many rows and columns as there are criteria; the diagonal of this table is directly each criterion's own highest share.

Fourth, calculating the loss. For each criterion, its highest share is compared against the share held, on that same criterion, by the alternative that is best on some other criterion. The difference is scaled by that criterion's highest value, producing a loss proportion. A criterion compared against itself always yields zero loss.

Fifth, building the loss system. For each criterion, all its losses are summed, and this total is written, with a negative sign, as that criterion's diagonal value; the rest of the table consists of the losses from the fourth step. The result is a system in which every row sums to zero.

Sixth, solving the system. Setting this system to zero yields a set of equations with a single solution once the total is fixed; this rests on a 1974 theorem of Mirkin's. CILOS finds this solution using linear algebra.

Seventh, normalising. The solution is scaled so that it sums to 1; the result is the set of CILOS weights.

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

A CILOS weight does not measure how important a criterion is in the decision-maker's eyes; it measures how expensive it turns out, in this particular table, to sacrifice being best on that criterion. A weight of 0.33 does not mean "this criterion is a third of the decision"; it means "in this alternative set, the cost of missing out on being best on this criterion amounts to roughly a third of the total loss." The same criterion can take a quite different weight in a different alternative set, because the weight is a property of the relationship among the alternatives, not a fixed trait of the criterion.

For this reason, CILOS weights cannot be carried over to another study. If one alternative is best on every criterion at once (a single alternative leading everywhere), the loss structure degenerates and the weights become unreliable; in that case, add a new alternative to the table or switch to a different weighting source. If two criteria's weights sit close together, this shows that the alternatives carry a similar opportunity cost on those two criteria.

For this reason:

"CILOS showed that price is the most important criterion"

should be written as:

"In this alternative set, missing out on being best on price carried the highest cost; the CILOS weight of 0.33 reflects this opportunity cost, not the decision-maker's own order of priority"

Classical CILOS works with crisp data: one number per cell. Values must be positive. DecisionMind holds three members in the CILOS family alongside the base method: crisp CILOS, triangular fuzzy FCILOS and scenario-based SCENARIO-FUZZY-CILOS. If your data is "approximate" by expert judgement or given as a range, FCILOS is the one to look at.

You need alternatives in rows, criteria in columns, a positive number in every cell, and no empty cells; for each criterion you need to know whether more is better or less is better. No weights are entered; the method produces weights and hands them on to a ranking method. A minimum of two alternatives and two criteria is required; as the number of alternatives grows, which alternative is best on which criterion is determined more reliably.

CILOS is a suitable choice when no expert opinion is available, when experts cannot agree, or when the weight is meant to be derived from the logic of "the cost of sacrificing this criterion." It works well on tables of real measurements where alternatives are clearly distinguished from one another (procurement, facility selection, equipment comparison), because the loss structure then carries a clear signal.

The cases where it should not be used follow from its own philosophy. If a single alternative is best on every criterion at once, the loss matrix collapses to zero and the weights become undefined; CILOS reports this as an error rather than a defined weight. If the decision-maker openly regards one criterion as a priority, CILOS cannot see this, since the method looks only at the opportunity cost present in the data. If there are very few alternatives (two or three), which alternative is best on which criterion can come down to chance.

No expert opinion available or wanted, weight to be derived from "cost of sacrifice" logic → CILOS

Same logic but the data is fuzzy → FCILOS

Both opportunity cost and dispersion (entropy) should enter together → IDOCRIW

Correlation between criteria should be the basis → CRITIC

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

CILOS's chief advantage is that it derives weight directly from how alternatives stand relative to one another, needing no separate dispersion or correlation calculation. The opportunity-cost idea is easy to convey to a decision-maker: "what do you lose elsewhere if you choose to be best here" is a concrete question. No experts need to be gathered, which makes it practical for large or repeated assessments. Because it forms half of IDOCRIW, it also lends itself to being used together with entropy.

Its limitations stem from the same structure. First, the weights depend on the alternative set; adding or removing an alternative can change which one is best on which criterion, requiring every weight to be recalculated. Second, if one alternative is best on several criteria at once, the loss structure can degenerate; a comparative study by Chatterjee and Chakraborty (2024) found that objective weighting methods show differing stability in such cases. Third, the way cost criteria are converted (dividing by the smallest value) affects the outcome; a different conversion can give different weights. Fourth, "importance" and "opportunity cost" are not the same thing; the decision-maker's own values are not reflected in the method.

The most common mistake is reporting a CILOS weight as "importance." The sentence "CILOS proved that price is the most critical criterion" is wrong; CILOS shows that missing out on being best on price carries the highest cost.

A second mistake is feeding cost criteria into the calculation without converting them first; the most expensive alternative is then treated as "best" and the loss structure runs in reverse. A third is ignoring the error CILOS returns when a single alternative is best on every criterion and forcing a weight out regardless; in that case the data should be reviewed afresh. A fourth is using the weights from this table in another study's different alternative set. A fifth is placing excessive trust in weights drawn from a small table of two or three alternatives.

The governing principle is this:

A CILOS weight measures how expensive sacrificing a criterion turns out to be within this particular alternative set; the weight changes when the alternative set changes, and the report must call this "opportunity cost," not "importance."