APLOCO (Approach of Logarithmic Concept)

The name APLOCO comes from "Approach of Logarithmic Concept" and belongs to a multi-criteria decision method introduced by Tevfik Bulut in 2018. DecisionMind's current APLOCO implementation carries this name but does not apply the logarithmic transformation step from Bulut's paper. Instead, it uses a scoring scheme that evaluates alternatives through pairwise comparison, summing the margins by which one alternative outperforms another on each criterion. The reason for this difference, and DecisionMind's own note on the matter, are set out in full in Case 1's source line and in the approval notes. Its output is a net superiority score for each alternative and the ranking that score produces; it ranks alternatives, it does not sort them into groups, and it does not generate criterion weights.

DecisionMind's calculation under the APLOCO name sets up a tournament logic. Every alternative is compared, one at a time, against every other alternative that remains. Where an alternative leads a rival on a criterion, that margin is multiplied by the criterion's weight and added in; where it trails, the margin on that criterion does not enter the calculation at all. This produces a one-way superiority score between two alternatives. An alternative's final score is found by subtracting the superiority it loses to all its rivals from the superiority it gains against them.

This structure has a consequence: the scores always sum to zero. However far one alternative pulls ahead, the rest fall behind by the same total, much as in a tournament scoreboard. The method is compensatory, because a shortfall on one criterion can be offset by strength on another. But unlike TOPSIS, its reference point is not an ideal alternative; it is the rivals themselves.

The APLOCO implementation used by DecisionMind proceeds through three steps.

First, scale equalisation. Every criterion column is rescaled to between 0 and 1 relative to its own minimum and maximum. For a "higher is better" criterion, the largest value becomes 1 and the smallest 0; for a "lower is better" criterion this is reversed. Criteria measured in different units become comparable on the same scale as a result.

Second, pairwise superiority. APLOCO compares every pair of alternatives. Where an alternative leads its rival on a criterion, that margin is multiplied by the criterion's weight; where it trails, its contribution is zero. These margins are summed across all criteria to give that pair's superiority score. The same calculation is run in the reverse direction too, so two alternatives produce two separate superiority scores between them.

Third, the net score. From the superiority scores an alternative gains against all its rivals, the superiority scores its rivals gain against it are subtracted. Alternatives are then ranked from the highest net score to the lowest.

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

The net score shows how far an alternative stands out from its rivals within this particular alternative set; it says nothing more than that. The scores always sum to zero, so a positive score means "above its rivals' average," a negative score "below it." The size of the score depends on the weighted differences between criteria and does not sit on a fixed scale such as 0 to 1; it cannot be compared with a score from a different analysis.

A small score gap, such as 0.45 against 0.00, can easily switch places once the alternative set changes, because every score is derived relative to all the other alternatives. Thus instead of writing:

"APLOCO found Alternative A to be the best"

the report should read:

"With this alternative set and these weights, Alternative A holds a net advantage over its rivals; the ranking is sensitive to the weight on this criterion"

APLOCO works with crisp data: one number per cell. DecisionMind currently carries no extension of this method for fuzzy, grey or other data types; if your data is approximate, given as a range, or based on expert opinion, a different family member should be sought.

You need alternatives in rows, criteria in columns, one number per cell, and no empty cells. Direction information is required for every criterion, whether more or less is better. APLOCO does not produce weights, it takes them from outside; the weights must sum to 1, and their source must be stated in the report. A minimum of two alternatives and two criteria is required; three to twelve criteria work comfortably. A criterion carrying the same value across every alternative, a constant column, drives the scale-equalisation step into a division by zero; such a column must be removed before the analysis.

APLOCO is a suitable choice if your criteria can be measured numerically, your table is complete, and you accept that a weakness on one criterion may be offset by strength on another. Its typical territory is supplier and alternative comparison. Where no compromise is ever acceptable on one criterion, or where criteria are strongly linked (one rising automatically as another rises), that link must be dealt with first; where necessary, a method built on elimination logic should be used instead.

A numerical table, compensation accepted, the goal is ranking → APLOCO

No compromise on one criterion, sub-threshold alternatives must be screened out → screening first, then ranking

"Superiority over rivals" rather than "closeness to the best" is wanted → APLOCO; distance to an ideal point is wanted → TOPSIS, Compromise Programming

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

The pairwise-comparison logic is intuitive: a decision-maker can follow the question "by how much does A lead B on these criteria?" directly. The computational burden is light, and the method works the same way as the number of alternatives grows. Because the scores always sum to zero, the result reads like a tournament table and shows at once which alternatives finish above or below the average.

Its limitations come from the form of normalisation and from the pairwise-comparison structure. Because columns are scaled relative to that analysis's own minimum and maximum, adding an alternative to the set afterwards can change the result. This is a known sensitivity, called rank reversal, in methods that use min-max normalisation (García-Cascales and Lamata, 2012). There is, moreover, no separate rank-reversal or comparative-study literature for this pairwise-superiority calculation as implemented by DecisionMind under the APLOCO name; the method's own behaviour has not yet been tested by independent studies. The assumption of full compensation also holds here: a serious weakness on one criterion can be papered over by others. The quality of the weights lies outside the method itself; a flawless calculation built on poor weights still produces a poor ranking.

The most common mistake is marking criterion direction wrongly; if a "lower is better" criterion is treated as "higher is better," scale equalisation runs in reverse and the net scores lose their meaning. A second mistake is assigning equal weights without justification; this is itself a choice and must be defended in the report. A third is reading the net score as a percentage or as a value on a fixed 0-to-1 scale; the score only makes sense within this particular alternative set. A fourth is adding an alternative once the analysis is finished and being surprised the ranking shifts. A fifth is failing to notice a constant-valued criterion column before normalisation.

The governing principle is this:

An APLOCO net score is a tournament summary of the directions, weights and alternative set you supplied; if any one of these inputs is contested, the ranking is contested too.