MPSI (Modified Preference Selection Index)

MPSI is not a ranking method: it does not rank alternatives, it produces criterion weights. It descends from the Preference Selection Index (PSI) method that Maniya and Bhatt proposed in 2010 for materials selection. The original PSI ranks alternatives directly, and while computing that ranking it internally assigns every criterion an implicit weight-like value; MPSI separates this implicit value from the rest of PSI and offers it on its own as a weight vector. The work that named this separation and introduced it as MPSI is an encyclopaedia chapter by Demir (2026).

If you hold a numerical decision table of alternatives and criteria, MPSI asks nobody which criterion matters more; it looks at the table's own internal spread and produces a weight vector that sums to 1. These weights then feed into a ranking method such as TOPSIS or VIKOR.

Most objective weighting methods, entropy and CRITIC among them, start from the same principle: the more the alternatives diverge on a criterion, the more that criterion drives the decision, so a wider spread earns a larger weight. The PSI logic that MPSI inherits does the opposite. If the sum of squared deviations from a criterion's column mean is large, meaning the alternatives diverge sharply on that criterion, MPSI assigns that criterion a comparatively lower weight; if the alternatives sit close together, the weight rises.

There is a reason for this. PSI's actual purpose is to rank alternatives, and a criterion that already diverges sharply creates a large difference of its own accord in the raw, normalised table. Rather than magnifying that difference a second time through a weight, PSI reins it in, so that no criterion comes to dominate the ranking disproportionately merely because of its own spread. When MPSI extracts this restraining value and presents it as a weight, the result reads as "the more the alternatives agree on this criterion, the more it can be trusted." This inverted logic is the central point that separates MPSI from the entropy and CRITIC family, and it must be spelled out in the report; otherwise the reader interprets the weight as they would an entropy weight, and is misled.

The method proceeds through three steps.

First, scale equalisation. In a "higher is better" criterion, every value is divided by the largest value in its column; in a "lower is better" criterion, the smallest value in the column is divided by every value. The result is a table in which the best alternative takes the value 1 on every criterion.

Second, the preference variation value. For each criterion, the mean of the equalised column is found, and then the squared deviation of every value from that mean is summed. This sum shows how much the alternatives diverge on that criterion; the PSI literature calls it the preference variation value.

Third, the weight. Each criterion's preference variation value is subtracted from one, and this difference is divided by the sum of the differences calculated across all criteria. A criterion with little divergence keeps a large difference, and so a large share; a criterion with much divergence has a smaller difference, and so a smaller share.

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

The MPSI weight does not measure a criterion's importance in the decision-maker's eyes; it measures how closely the alternatives behave towards one another on that criterion, running in the opposite direction from entropy and CRITIC. A weight of 0.34 does not mean "this criterion is a third of the decision"; it means "the alternatives are relatively in agreement on this criterion, and this criterion is not meant to dominate the ranking on its own." If the alternatives carry very different values on a criterion, that criterion's MPSI weight comes out low; this does not mean the criterion is unimportant, but rather that it already creates a large effect of its own in the normalised table and does not need to be magnified further by an additional weight.

The case where every alternative carries the same value on a criterion (a constant criterion) forms a special exception in MPSI: because the deviation is zero, that criterion's difference stays exactly at 1, and the criterion receives an average-level weight rather than zero. This differs from entropy and CRITIC, where a constant criterion's weight falls to zero, and the report should state this difference explicitly.

Therefore, instead of writing:

"The MPSI analysis showed that cost was the least important criterion"

the report should read:

"The alternatives were the group most divergent from one another on the cost criterion; MPSI assigned cost a comparatively low weight so as not to magnify this divergence a second time, not because the criterion is unimportant"

Classical MPSI works with crisp data: one number per cell. Values must be positive; zero and negative values can cause problems in the scale-equalisation step. DecisionMind does not currently hold a separate extension of MPSI; it stands as a single member, though the PSI family it descends from has members for other data types such as fuzzy and intuitionistic fuzzy data.

You need alternatives in rows, criteria in columns, one positive number per cell, and no empty cells; for every criterion, whether more is better or less is better, since scale equalisation is done according to this direction. Weights are not entered; the method produces them. A minimum of two alternatives and two criteria is required; as the number of alternatives grows, the deviation sum is computed more stably.

MPSI is a consistent choice specifically when a study already ranks alternatives with PSI and also wants the weights derived from the same logic, from the same method family. Where there is no expert opinion and the decision-maker wants a criterion's already-large spread among alternatives not to be magnified a second time by a weight, MPSI suits well.

The cases where it should not be used follow from its philosophy. If the decision-maker's habitual expectation is "high spread, high weight" (as with entropy or CRITIC), MPSI's opposite direction creates confusion, and the report must explain this. Where the decision-maker clearly regards one criterion as a priority, MPSI cannot see that. With few alternatives, the deviation sum can be computed unreliably.

A weight consistent with the PSI family is wanted, no expert opinion available → MPSI

High spread should mean high weight → Entropy, CRITIC

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

Both preference and data matter → a combination of subjective and objective weights

MPSI's most important advantage is that it makes ranking and weighting consistent within the same method family as PSI; where a study both ranks with PSI and wants weights displayed, a single logic can be used instead of two separate methods. The calculation is simple and requires no advanced statistics. Keeping a constant criterion at an average level rather than zeroing it out prevents that criterion from disappearing entirely from the table in some applications.

Its limitations stem from the same inverted logic. First, the "low divergence, high weight" relationship runs opposite to the entropy logic most readers are used to; if the report does not explain this, it will be misread (Chakraborty, Chatterjee and Das, 2023). Second, the weights depend on the alternative set: adding or removing an alternative changes the deviations, and so the weights. Third, the MPSI name and its introduction as a separate weighting method are recent; independent comparison and critique literature is still limited. Fourth, it cannot work directly with zero or negative values.

The most common mistake is reading the MPSI weight the way one would read an entropy weight; reporting it with the expectation of "high weight, high spread" is exactly the wrong way round in MPSI, because in MPSI high spread corresponds to low weight.

A second mistake is marking criterion direction wrongly; if a "lower is better" criterion is marked "higher is better," scale equalisation runs backwards and the deviation sum is computed incorrectly. A third mistake is treating a constant criterion's average-level weight as a "method error"; this is MPSI's defined behaviour. A fourth mistake is using one study's MPSI weights on a different alternative set. A fifth is confusing the MPSI weight with PSI's own ranking score (I_i); the two are different outputs.

The governing principle is this:

The MPSI weight measures how much the alternatives agree on a criterion; a high weight does not mean "the criterion is important" but "the alternatives are close to one another on this criterion, so there is no need to magnify it a second time with weight."