IDOCRIW (Integrated Determination of Objective Criteria Weights)

IDOCRIW is not a ranking method; it does not rank alternatives, it produces criterion weights. It looks at the decision table and, without asking the expert anything, gives every criterion a weight, with the weights summing to 1. These weights then feed into a ranking method such as TOPSIS, COPRAS or SAW.

Zavadskas and Podvezko proposed the method in 2016. IDOCRIW is not, in itself, a wholly new calculation; it combines two separate objective methods, entropy and CILOS (Criterion Impact LOSs), introduced in the same paper. The idea is that each method covers the other's weak point: entropy looks only at how spread out the data is, and cannot see what disregarding a criterion would cost on the other criteria; CILOS measures this loss but, used alone, can overlook the data's overall spread. IDOCRIW takes the product of the two to produce a single weight.

Behind IDOCRIW lie two separate questions. The first comes from entropy: "how different are the alternatives from one another on this criterion?" The second is specific to CILOS: "if an alternative is preferred because it is best on this criterion, how much is lost on the other criteria?" CILOS sets this up as follows: for each criterion, the alternative carrying the best value is identified, a hypothetical reference is built from these alternatives, and then how far "behind" each criterion's best alternative falls on the other criteria is measured. If a criterion's best alternative causes large losses on the other criteria when chosen, disregarding that criterion is costly, and it receives a high weight.

The consequence of this philosophy is that IDOCRIW does not stop at asking "how spread out is the data" but also asks "what is the cost of favouring this criterion." Because the two measures are multiplied together, a criterion receives a high weight only if it is both discriminating and costly to disregard; either alone is not enough. This tends to soften the extreme weights that entropy or CILOS alone might give.

The method proceeds through three steps.

First, entropy weights. On the raw table, each column is converted to a share by dividing by its own column sum, and Shannon entropy is computed for every criterion. If the shares are close to one another, entropy is high and the criterion carries little information; if the shares are concentrated in one alternative, entropy is low and the criterion carries a great deal of information. The information content derived from entropy is normalised to give a set of weights. This is the same calculation described in the ENTROPY card.

Second, criterion impact loss (CILOS). Every criterion is converted to a benefit orientation; for cost criteria, the smallest value is taken as the reference. For every criterion, the alternative carrying the best value is found, and these "best" values are gathered together to build a hypothetical reference row. The proportional difference between each criterion's best alternative and that alternative's value on every other criterion is then computed; this difference shows the loss, on other criteria, that favouring that criterion causes. A system of equations built from all these losses is solved to obtain the CILOS weights.

Third, combining. The entropy weight and the CILOS weight are multiplied together for each criterion, and the result is renormalised to give an IDOCRIW weight vector summing to 1.

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

An IDOCRIW weight reflects both a criterion's discriminating power in the data and the loss that would follow from disregarding it; it does not measure importance in the decision-maker's eyes. A weight of 0.35 does not mean "this criterion is a third of the decision"; it means "in this table, this criterion both distinguishes the alternatives markedly and its being set aside would cause a serious loss." If a criterion's entropy weight is high but its CILOS weight low (or the reverse), the IDOCRIW weight, being their product, ends up somewhere in between; this is a consequence of the method balancing the two measures.

Weights depend on the table. When the alternative set changes, both the entropy and the CILOS component are recomputed; a study's IDOCRIW weights cannot be carried over to another study. If all of a criterion's loss values are zero (that is, no alternative falls behind another on that criterion), the CILOS component can become undefined; DecisionMind reports this error explicitly rather than silently assigning equal weight.

Thus instead of writing:

"The IDOCRIW analysis showed that the quality criterion is the most important criterion"

the report should read:

"In this option set, the quality criterion both discriminates the alternatives the most and is the most costly to disregard; the weight reflects these two measures together, not the decision-maker's priority order"

Classical IDOCRIW works with crisp data: a single number per cell, no empty cells. DecisionMind treats a fuzzy extension (Fuzzy IDOCRIW) of this method as a separate card; if your data is given as triangular fuzzy numbers from expert judgement, consult that card instead. Because of the entropy component, values must not be negative, and because of the CILOS component, a genuine difference between alternatives is required on every criterion; a column where all alternatives are equal breaks the CILOS calculation.

You need the following: alternatives in rows, criteria in columns, a positive number in every cell; and, for every criterion, whether more is better or less is better. Weights are not entered; the method produces them. A minimum of two alternatives and two criteria is required; as the number of criteria grows, the system of equations CILOS solves grows too, but the calculation is still solved directly, with no upper bound on sample size.

IDOCRIW is a suitable choice if expert opinion is unavailable, or if you do not want the decision-maker's priorities to determine the result. It is particularly suitable when you want to look not only at the data's spread but also at the loss that would follow from disregarding a criterion. It works well in tables that are both measurable and contain genuine differences between alternatives, such as procurement, facility and equipment evaluation.

The situations in which it should not be used follow from its own philosophy. If all the alternatives are very close to one another on a criterion, the loss calculation CILOS depends on weakens or becomes undefined. Where the decision-maker clearly regards one criterion as a priority, IDOCRIW cannot see this, because it relies entirely on the data. If there are fewer than two criteria, the system of equations CILOS builds does not yield a meaningful solution.

No expert opinion, both discrimination and disregard-loss should be measured → IDOCRIW

Discrimination alone is sufficient → Entropy

Only inter-criterion relationship (redundancy) matters → CRITIC

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

No genuine difference between alternatives on a criterion → remove that criterion, or the CILOS component may remain undefined

IDOCRIW's greatest strength is combining two different objective viewpoints, spread and loss, into a single weight. It accounts for something entropy alone would miss: the cost, on other criteria, of disregarding a given criterion. It is objective, giving the same table the same weight for everyone. The product of the two components tends to soften the excessive weight a single measure might otherwise give. Its calculation can be followed step by step, and both components can be reported separately.

Its limitations arise from the same composite structure. First, because it is the product of two different measures, a problem in a single component (for instance, CILOS remaining undefined on one criterion) can spoil the whole weight. Second, "discrimination and loss" is not the same thing as "importance"; the decision-maker's values do not appear in the result. Third, the weights depend on the alternative set; adding an alternative rebuilds both the entropy and the CILOS component. Fourth, CILOS's reference alternative (the hypothetical row carrying the best on every criterion) does not actually exist; this is an abstraction similar to the ideal point in TOPSIS and rests on the same kind of assumption. As Podvezko, Zavadskas and Podviezko's (2020) fuzzy-extension study also notes, the CILOS component can give more volatile results when the data contains few alternatives. Ayan, Abacıoğlu and Basilio's (2023) review notes that composite objective methods (IDOCRIW included) can produce more complex, but also less transparent, results than single-component methods.

The most common mistake is reporting the IDOCRIW weight directly as "importance"; the weight measures the product of the discrimination and loss components, not the decision-maker's priority.

A second mistake is leaving a column in the table, unnoticed, where all the alternatives are very close to one another; in this case the CILOS component can remain undefined, and although DecisionMind reports the error, a user may misread this as "the method is not working." A third mistake is looking only at the final weight without examining the entropy and CILOS components separately; without seeing how the two components balance each other, the reason for the result cannot be understood. A fourth mistake is taking IDOCRIW weights from one study and applying them to a different alternative set. Fifth is marking the cost and benefit directions incorrectly; this spoils both the entropy and the CILOS component at once.

The governing principle is this:

An IDOCRIW weight is the product of two separate objective measures, the data's discriminating power and the loss from disregarding a criterion; a high weight shows the criterion satisfies these two measures together, not its importance to the decision-maker.