Scenario-Based Fuzzy CILOS

This card describes a profile within DecisionMind's CILOS family; it is not an independent, separately published method. Its basis is classical CILOS (Criterion Impact LOSs), the objective weighting method proposed by Zavadskas and Podvezko in 2016, which derives criterion weight from the logic of "how much being best on one criterion costs an alternative on the others." CILOS is defined for crisp data; when data is instead supplied by expert judgement as a triangular fuzzy number (a lower, middle and upper value), CILOS cannot be applied directly.

DecisionMind fills this gap in more than one way. FCILOS, published by Podvezko, Zavadskas and Podviezko (2020) and held as a separate member in DecisionMind, rebuilds CILOS from the ground up in fuzzy arithmetic and is directly tied to the literature. Scenario-Based Fuzzy CILOS is a simpler, separate profile built on an engineering decision: it treats the triangle's three corners as three independent crisp tables, runs classical CILOS on each in turn, and averages the three results. This profile has no peer-reviewed founding paper of its own; it is an implementation developed by the DecisionMind team and currently under review, and this card states that plainly.

CILOS's philosophy is this: obtaining the best alternative on one criterion is rarely free of cost, because that alternative may fall behind on others. CILOS asks, for every criterion, "how much does the alternative that is best on this criterion lose on the others," and gives greater weight to criteria where this loss is large, because being good on such a criterion genuinely requires giving something up, which makes that criterion more decisive in the choice.

Scenario-Based Fuzzy CILOS does not change this logic; it only simplifies how it is applied to fuzzy input. A triangular fuzzy value represents a range in which an expert says, in effect, "at worst this, most likely this, at best this." This profile treats the three possibilities as three separate scenarios: it runs CILOS independently under "everything goes badly" (the lower corner), "things go as expected" (the middle corner) and "everything goes well" (the upper corner), producing three separate weight sets, then averages them. This is an approach that is easy to compute and easy to follow, but because it treats the three corners as three independent crisp problems, it does not fully capture the triangle's own internal structure, that is, how the three corners TOGETHER form a single uncertainty. This differs from the path followed by canonical fuzzy CILOS (Podvezko et al., 2020), which preserves fuzzy arithmetic throughout.

The method proceeds through three steps.

First, input validation. For every cell, the triangular fuzzy number (lower, middle, upper) supplied by the expert is recorded, together with each criterion's direction (whether more or less is better).

Second, three separate classical runs. The lower-corner values are taken as one crisp decision table, and all of classical CILOS's steps (rescaling, building the loss matrix, solving the linear system) are applied to it to obtain one weight set. The same procedure is then repeated separately with the middle-corner values and with the upper-corner values, yielding three independent weight sets.

Third, averaging and reporting. The three weight sets are averaged criterion by criterion and renormalised so that they sum to 1. DecisionMind additionally reports how far the three scenarios diverge from one another, that is, how far the fuzziness has shifted the result.

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

The output is the average weight of the three scenarios (worst, expected, best); it is read in the same way as a classical CILOS weight, meaning it reflects not the criterion's importance in the decision-maker's eyes but the size of the loss that being best on that criterion imposes on the other criteria. If the three scenarios' weights sit close together, this generally means that the uncertainty in the expert's estimate, that is, the triangle's width, has not much changed the result; if the three scenarios differ markedly, the uncertainty has carried through into the weights, and the report must show this difference.

There is a specific case seen in this profile's validation fixture: if a single alternative comes out best on every criterion at once, CILOS's loss matrix collapses entirely to zero, and the equation system yields an undifferentiated, evenly spread weight. This is not a computational error; it is a natural consequence of CILOS's own logic, because "the cost of being best" was never actually incurred on any criterion in that data set. When such a result appears, the weights should be read not as "the criteria are equally important" but as "no real trade-off was observed for any criterion in this data set."

Thus instead of writing:

"The Scenario-Based Fuzzy CILOS analysis showed that all three criteria are equally important"

the report should read:

"No real trade-off was observed for any criterion in this alternative set, which is why the weights came out equal; a different alternative set may change the result"

Scenario-Based Fuzzy CILOS is for situations in which the data is given as a triangular fuzzy number (lower, middle, upper); it is an extension of classical crisp CILOS. DecisionMind holds two separate members of the CILOS family for fuzzy data: FCILOS, directly tied to the literature, and Scenario-Based Fuzzy CILOS, the subject of this card, developed in-house by DecisionMind. The two can give different results for the same input; where a literal comparison with the literature is required, FCILOS should be preferred.

You need alternatives in rows, criteria in columns, a triangular fuzzy number from expert judgement (worst, most likely, best) in every cell, and no empty cells. Direction information ("more is better" or "less is better") is required for every criterion. No weights are entered; the method produces the weights. A minimum of two alternatives and two criteria is required; for the equation system in CILOS to have a meaningful solution, at least some genuine trade-offs must exist among the criteria.

This profile is currently under review by the DecisionMind team, and its maturity is flagged as "deferred." Where expert estimates have been obtained as triangular fuzzy numbers and a quick, easily traced attempt at fuzzy CILOS is wanted, it can be used provided that the result is clearly stated not to rest on a canonical literature source.

The cases where it should not be used follow from its philosophy and its current status. Where a fuzzy CILOS result that can be compared directly with the literature and rests on a peer-reviewed source is required, FCILOS should be preferred. On (degenerate) data sets where a single alternative comes out best on every criterion at once, this profile can give an undifferentiated, equal weight; when such a result appears, the data set should be reviewed. Where the decision rationale is to underpin a formal report or a publication, this profile's experimental status must be stated clearly to the reader.

A quick, easily traced attempt at fuzzy CILOS, with the result labelled as experimental → Scenario-Based Fuzzy CILOS

A fuzzy CILOS that matches the literature exactly is required → FCILOS

Data is crisp, not fuzzy → Classical CILOS

A single alternative comes out best on every criterion (degenerate data) → the data set should be reviewed; the result may be undifferentiated

This profile's greatest advantage is its simplicity: solving the three corners separately with classical CILOS and averaging them is easy to compute and easy to trace, and each scenario can be audited on its own. Showing how far the three scenarios diverge quickly reveals how much the uncertainty in expert estimates has carried through to the result. It is one of the most readily understood ways of carrying classical CILOS's logic across to fuzzy data without altering it.

Its limitations stem largely from the profile's own design and current status. First, this profile has no direct counterpart in the literature; it is the DecisionMind team's own engineering decision, which is a disadvantage for work that will underpin a publication. Second, solving the three corners as three independent crisp problems and averaging them does not fully capture the uncertainty structure that the triangle's three corners form TOGETHER; canonical fuzzy CILOS (Podvezko, Zavadskas and Podviezko, 2020) follows a different mathematical path and can give a different result on the same input. Third, on data sets where a single alternative comes out best on every criterion at once, the loss matrix collapses to zero and the weights fall into an undifferentiated distribution; this has been observed in DecisionMind's own validation fixture, and while the classical CILOS kernel raises an error in such a case, this profile currently produces an equal weight without stopping. Fourth, where the triangular fuzzy number is given proportionally, that is, with every corner scaled by the same ratio, the three scenarios' weights usually come out very close to one another, in which case it is debatable whether the fuzziness has genuinely added anything.

The most common mistake is reporting this profile's result as though it were the same method as canonical fuzzy CILOS (Podvezko et al., 2020); the two follow different mathematical paths and can give different results.

A second mistake is presenting the solving and averaging of the three corners separately as though the fuzziness were "fully modelled"; this approach represents fuzziness approximately, not exactly. A third mistake is reading equal weights obtained on a degenerate data set as "the criteria are equally important"; this is usually a sign that no real trade-off exists in the data set. A fourth mistake is hiding this profile's experimental status from the reader; the DecisionMind team is reviewing this profile, and the report must state this.

The governing principle is this:

A Scenario-Based Fuzzy CILOS result is the output of an engineering approach, not a method verified against a peer-reviewed literature source; the report must state this plainly and, where warranted, compare it against FCILOS.