PSI (Preference Selection Index)

PSI is a ranking method for situations where you already hold a decision table but do not want to assign weights to the criteria. It also serves you well when you simply have no grounds for assigning weights. Its output is a preference score for every alternative, the rank that score produces, and the criterion weights the method itself generates. Maniya and Bhatt proposed it in 2010, originally for a material-selection problem, and the literature treats it as one of the few MCDM methods that dispenses with the weighting stage entirely.

PSI's underlying idea runs as follows: if alternatives take widely different values on a criterion, that criterion is already self-distinguishing and needs no extra weight; but if alternatives take similar values on a criterion, that criterion cannot separate the alternatives on its own and its contribution to the total score risks being drowned out. PSI reverses this: it rewards a criterion on which alternatives differentiate LESS with a relatively HIGHER weight, so that it is not lost in the total. This is the exact opposite of the logic behind Entropy or CRITIC, where "a criterion that spreads more is more informative and deserves a higher weight."

This idea carries a philosophical consequence. In PSI, weight is not the criterion's importance in the decision-maker's eyes; it is a product of the data's own distribution. In methods that ask for weights, such as TOPSIS, MAUT, RAFSI or RAWEC, a weight is a stated preference and must be defended. In PSI, weight is a statistical outcome; the answer to "why this weight" is "because the data happen to be distributed this way." That answer reflects the structure of the current alternative set, not the decision-maker's priorities.

The method proceeds through four steps.

First, scale equalisation (linear normalisation). The method normalises every criterion according to its own direction: for "higher is better" criteria it divides every value by the column maximum, and for "lower is better" criteria it divides the column minimum by every value. Every column then fits between 0 and 1, with the best value always equal to 1.

Second, measuring each criterion's own internal spread. The method takes the mean of each column, then computes and sums the squared deviation of every value from that mean. This sum shows how much the alternatives differ from one another on that criterion; a large sum means the alternatives are widely scattered on it.

Third, computing the preference variation value and the self-derived weights. For every criterion, the method subtracts the second step's spread measure from 1; this value shrinks for a widely spread criterion and grows for a narrowly spread one. The method sums these values across all criteria, turns each into a share of that sum, and uses the share directly as the criterion weight. No external weight input is required at any point. DecisionMind runs this step fail-closed: if any value comes out negative or undefined, or if the sum falls to zero or below, the engine halts the calculation rather than produce an invalid weight.

Fourth, computing the preference selection index and ranking in descending order. The method multiplies every normalised value by its criterion's derived weight and sums them; alternatives are then ranked by this index from highest to lowest.

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

The preference selection index tells you how preferable an alternative is relative to the other alternatives in this table, and nothing more. A score of 0.86 does not mean "86 per cent good," and it cannot be compared with a score from a different analysis, because both the normalisation and the weights are derived from this particular alternative set. The criterion weights are likewise specific only to this table. A criterion receiving a low weight does not mean that criterion is unimportant in the decision-maker's eyes; it means the alternatives differentiate little on it. This distinction must be made explicit in the report, otherwise a safety or compliance criterion that happens to receive a low weight can be misrepresented as "unimportant."

Thus instead of writing:

"PSI showed that the quality criterion is unimportant"

the report should read:

"In this alternative set, the alternatives took similar values on the quality criterion, so PSI assigned it a relatively low weight; this reflects low discriminating power, not unimportance"

Classical PSI works with crisp data: one number per cell, no empty cells. If your data is fuzzy, intuitionistic fuzzy, neutrosophic, or contradictory across experts, DecisionMind holds four PSI family members alongside the base method: fuzzy, neutrosophic and plithogenic extensions. This count excludes MPSI (Modified PSI). MPSI does not produce weights; it is a different version of PSI built for a different purpose, namely objective weighting.

You need alternatives in rows, criteria in columns, one number per cell, and for every criterion whether higher or lower is better. PSI does not ask for weights, it produces them itself, so there is no need for a subjective weighting step such as AHP, BWM or SWARA, nor for a separate objective weighting step such as Entropy or CRITIC. A minimum of two alternatives and two criteria is required; three to twelve criteria work comfortably. A zero value is not accepted for cost criteria, as it carries a division-by-zero risk; for benefit criteria, zero is defined only when the column maximum is positive.

PSI is a suitable choice when you have neither expert judgement nor sufficient historical data to justify weighting the criteria. Using it means accepting the existing spread among alternatives as a priority signal. Its typical territory includes material and process-parameter selection, rapid preliminary assessments, and situations where debating weights would waste time.

There are two situations where it should not be used. First, if the criteria's importance is already clear to the decision-maker and rests on the decision-maker's values rather than the data, PSI is unsuitable: it disregards that preference and imposes a weight derived from the data instead. Second, if a low-spread criterion is actually a critical threshold or compliance criterion (a safety standard, say), PSI is again unsuitable: it reads that criterion's low spread as "high weight" rather than "of little importance," and the result can be misread if the decision-maker's actual priority differs.

No expert or historical basis for weighting, a quick objective weight is wanted → PSI

Weights must reflect the decision-maker's known priorities → AHP, BWM, SWARA (subjective)

Weights should be objective, but on the logic that a wider-spread criterion is more informative → Entropy, CRITIC

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

Weights already exist, only ranking is needed → TOPSIS, VIKOR, SAW

PSI's greatest strength is that it removes the weighting process entirely. There is no need to gather expert opinion, run pairwise comparisons, or carry out a separate objective weighting step; the method produces both the weights and the ranking in a single computational chain. The computational burden is small, and every step can be followed on the table. When debate over weights causes disagreement among decision-makers or time is short, PSI offers a practical solution for rapid preliminary assessments (Attri and Grover, 2015).

Its limitations stem from the weight-generating mechanism itself. First, the weights reflect the data's distribution rather than the decision-maker's preference; a critical but narrow-spread criterion can wrongly receive a relatively high weight, as happens with a safety threshold that every alternative already meets, even though the decision-maker regards it as a pass/fail threshold not expected to discriminate. Second, the weights depend on the alternative set: adding or removing an alternative changes not just the ranking but the weights themselves, which makes the result harder to reproduce. Third, a "modified PSI" (MPSI) has since been derived from the method, showing that PSI's original weighting logic is still debated in the literature and remains open to development (Demir, 2026). Fourth, PSI shares TOPSIS's assumption of full compensation: a weakness on one criterion can be masked by another.

The most common mistake is reading a low weight PSI produces as "this criterion is unimportant," when a low weight only shows that alternatives are close to one another on it. A second mistake is using PSI where weights ought to reflect the decision-maker's priorities; if, for instance, senior management explicitly prioritises one criterion, a subjective weighting method is needed instead of PSI. A third mistake is carrying old weights over to a new table once the alternative set has changed; in PSI, weights must be recalculated together with the table. A fourth is proceeding with the calculation when a cost criterion contains a zero value; this carries a division-by-zero risk, and the engine must halt fail-closed in that case. A fifth is reading the preference score as a percentage or a probability, or comparing scores across different analyses.

The governing principle is this:

PSI's weights summarise how the data happen to be distributed within the current alternative set, not the decision-maker's priorities; if the alternative set or the data itself is contested, the weights are contested too, and the report must show this.