QUALIFLEX (Qualitative Flexible Multiple Criteria Method)

QUALIFLEX is a ranking method for arranging alternatives into a single order once you already hold a numerical decision table. Its output is a rank position for every alternative; unlike TOPSIS or PROBID, it does not produce an interval score, but answers the question "which ordering is best" directly. Paelinck proposed it in 1978 for regional-economics decisions, as a flexible method able to handle both numerical and ordinal information together. Its name comes from the abbreviation "Qualitative Flexible."

Most ranking methods, such as TOPSIS, PROBID or SAW, first assign a score to every alternative and then rank by that score. QUALIFLEX reverses the order: it first tries every possible ordering, then measures how well each ordering agrees with the criteria. Three alternatives yield six possible orderings; four alternatives yield twenty-four; the method tries every one of them in turn.

This idea carries a philosophical consequence: QUALIFLEX is a direct "search for the best ordering." For every candidate ordering, each pair of alternatives placed one above the other is checked, on every criterion, to see whether the higher-placed alternative is genuinely superior on that criterion; if so, a score equal to the criterion's weight is gained, and if not, it is lost. The sum of these scores is that ordering's "agreement score," and the ordering with the highest agreement score wins. The method remains compensatory, because disagreements between criteria can offset one another in the weighted sum, but its result is a ranking directly, not a score.

The method proceeds through two steps.

First, pairwise agreement for every possible ordering. Every possible ordering (permutation) of the alternatives is considered in turn. Within each ordering, for every pair consisting of a higher-placed and a lower-placed alternative, the method checks, on each criterion, whether the higher-placed alternative is genuinely better or worse; for "lower is better" criteria this comparison is reversed.

Second, total agreement and selection. The result of this pairwise comparison on each criterion is multiplied by the criterion's weight and summed across all criteria and all alternative pairs; this total is that ordering's "comprehensive agreement index." The ordering with the highest agreement index is the final ordering QUALIFLEX recommends.

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

QUALIFLEX's output is a ranking directly, not a score. DecisionMind assigns every alternative a "rank value" to make this ordering readable, the highest number going to the best alternative, but this value is not an interval score, it carries rank information only. The difference between two alternatives does not answer "how much better," only "which comes first."

The chosen ordering is whichever, among all orderings tried, achieves the highest agreement index; but how robust the result is remains unknown until you also report how close the second-best ordering's agreement index comes to it. If the gap in agreement index between two orderings is small, a small change in the data or the weights can change the winning ordering.

Thus instead of writing:

"QUALIFLEX found the correct ordering"

the report should read:

"With these weights and this alternative set, this is the ordering with the highest agreement index; how close the second-best ordering's index comes to it should also be checked"

QUALIFLEX works with crisp data: one number per cell. You need alternatives in rows, criteria in columns, direction information for every criterion, and criterion weights summing to 1. DecisionMind currently holds no extension of this method; it runs in its base crisp form. The literature also describes extensions of QUALIFLEX for fuzzy, intuitionistic fuzzy and interval-valued intuitionistic fuzzy sets (Chen, Chang and Lu, 2013; Zhang and Xu, 2015; Chen, 2014).

A minimum of two alternatives and two criteria is required. Because the method tries every possible ordering one by one, the computational burden grows very quickly with the number of alternatives: seven alternatives yield 5,040 orderings, eight yield 40,320, and ten yield 3,628,800. The method therefore runs most comfortably with a low number of alternatives, between three and fifteen; larger problems require heuristic search methods instead.

QUALIFLEX is a suitable choice when the number of alternatives is limited, your criteria can be measured numerically, and a direct ordering, rather than an interval score, is sufficient. It is preferable in decisions such as regional development or public-policy prioritisation, where several stakeholders debate the ordering while the underlying data remains numerical.

It should not be used where the number of alternatives is large or where an interval score is needed, one that conveys not just rank but "how much" of a difference. Beyond eight alternatives the computational burden grows rapidly; in that case a method that produces a score directly, such as TOPSIS or PROBID, should be preferred.

Few alternatives, an ordering alone is sufficient → QUALIFLEX

Many alternatives (more than eight) → score-producing methods such as TOPSIS, PROBID

An interval score is needed ("how much" of a gap matters) → TOPSIS, PROBID, SAW

Weights are needed rather than a ranking → AHP, BWM, SWARA (subjective) · Entropy, CRITIC (objective)

QUALIFLEX's greatest strength is that it selects the ordering directly from among the possible orderings, not through an indirect score; this bypasses assumptions introduced by intermediate normalisation steps, such as TOPSIS's vector normalisation. The method is designed to work with both numerical and ordinal data; Paelinck's original 1978 proposal was built to accommodate the mixed structure of regional-economics data. For small numbers of alternatives, the result comes from a complete search in which every alternative is compared against every other; it does not rely on a heuristic shortcut.

QUALIFLEX's most conspicuous limitation is its computational burden: the number of permutations grows factorially with the number of alternatives, making the method impractical for large problems. Second, the output is only a ranking; it gives no information about the size of the gap between two alternatives, which makes sensitivity analysis harder. Third, the method remains compensatory and can conceal disagreement between criteria within the weighted sum. Fourth, the original method is limited to crisp numerical data; separate extensions have been needed to work with uncertain or fuzzy data (Chen, Chang and Lu, 2013; Zhang and Xu, 2015).

The most common mistake is marking criterion direction wrongly; this reverses the sign of the pairwise agreement calculation and declares an entirely different ordering the winner. A second mistake is applying the method as the number of alternatives grows past eight without considering the computational burden. A third is presenting the winning ordering's agreement index as a "definitive result" without comparing it against the second-ranked candidate; if the gap is small, the ordering is fragile. A fourth is reading QUALIFLEX's rank value as a score and drawing percentage differences from it; this value carries rank information only.

The governing principle is this:

A QUALIFLEX result is the ordering that achieves the highest agreement with the weights you supplied, among all the orderings tried; if the gap between the winning ordering and the next-best ordering is small, the result is sensitive to the weights, and the report must show this.