PIPRECIA (Pivot Pairwise Relative Criteria Importance Assessment)

PIPRECIA is a method that assigns criterion weights from expert judgement. Its output is a weight vector summing to one; it does not evaluate alternatives. In SWARA, the expert must first rank the criteria by importance and then state how much less important each one is than the one before it; this requires knowing the answer to "which is more important" from the outset. PIPRECIA removes that requirement: criteria can be taken in any order (alphabetical, say, or the order in which data was collected), and each one is judged as more important, equally important, or less important than the one before it. Proposed by Stanujkić, Zavadskas, Karabašević, Smarandache and Turskis in 2017, the method is used in criterion-weighting work as a relaxed variant of SWARA.

PIPRECIA's underlying idea is that in real decision situations, experts can already form a judgement about each criterion even before ranking them by importance. SWARA says: "rank from most to least important, then state the gaps between them," which forces the expert to settle the ranking before the analysis begins, and a mistaken initial ranking colours the entire result. PIPRECIA, whatever order the criteria are taken in, asks only "how does this one compare with the previous one," and the answer can point in either direction: more important, equal, or less important. This turns the ranking into an output of the analysis rather than an assumption that has to be supplied beforehand.

This carries a consequence: in PIPRECIA, the order in which criteria are taken up (the pivot order) affects the result, because every comparison is made against the one before it. SWARA's "rank first" problem disappears, but in its place comes the question of whether the order of treatment affects the weights; the pivot order should therefore be chosen with reasons, not at random.

The method proceeds through three steps.

First, the relative importance coefficient. Criteria are taken in a fixed order; the first is treated as the reference and its coefficient is set at 1. For every criterion after that, the expert rates its importance relative to the one before it with a number between 0 and 2: 1 means equal importance, a value above 1 means more important than the previous criterion, and a value below 1 means less important than the previous criterion.

Second, the coefficient and the relative weight. For each criterion, a coefficient is derived from this relative-importance figure (2 minus the relative-importance number). The first criterion's relative weight is taken as 1; each subsequent criterion's relative weight is found by dividing the previous criterion's relative weight by this coefficient. When the relative-importance number is above 1 (the criterion is more important than the one before it), the coefficient shrinks and the relative weight grows; when the relative-importance number is below 1, the opposite happens.

Third, the normalised weight. The relative weights are divided by their own sum to produce criterion weights that add up to one.

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

A weight is the cumulative result of the relative-importance judgements made between consecutive criteria in the order they were taken up; a criterion's weight depends not only on its own judgement but on the judgements of every criterion that preceded it. The last criterion taken up tends to end up with the largest or the smallest weight, because it carries the multiplicative accumulation of every relative weight before it. This does not mean that criterion is "genuinely" the most or least important; it may simply be the final link in the order of treatment.

Thus instead of writing:

"PIPRECIA proved that this criterion is the most important"

the report should read:

"With the criteria taken in this order and these relative-importance judgements, this criterion received the highest weight; a different order of treatment could give a different distribution of weights"

PIPRECIA works with crisp data: one relative-importance number per criterion, between 0 and 2. DecisionMind does not hold a separately registered extension member within the PIPRECIA family; fuzzy and grey variants have been defined in the literature, but these are not held as a separate member in DecisionMind. You need at least two criteria, a fixed order in which the criteria are to be taken up, and, for every criterion after the first, a relative-importance number against the one before it. The method produces weights; it does not ask for weights from outside. Three to twelve criteria is typical.

PIPRECIA is a suitable choice if the expert struggles to place the criteria into a firm importance ranking beforehand, but can comfortably answer "more important, equal, or less important" for consecutive criteria. If the expert can already produce a clear importance ranking, SWARA is the more direct option. Where it is unacceptable for the order of treatment to affect the result — that is, where a weight independent of order is required — pairwise-comparison methods such as AHP or BWM should be preferred.

A firm prior ranking is hard, consecutive comparison is comfortable → PIPRECIA

A firm prior ranking can already be produced → SWARA

The result must not depend on the order of treatment → AHP, BWM

Not weights but the data's own variability matters → Entropy, CRITIC

PIPRECIA's greatest strength is that it removes SWARA's requirement of ranking beforehand; this gives a more flexible starting point when the expert does not yet have a clear sense of the ranking among criteria (Stanujkić et al., 2021). The method requires few consecutive comparisons; with n criteria, only n − 1 judgements are collected. The calculations are simple, and the intermediate steps (coefficient, relative weight) can easily be followed in a table.

The method's greatest limitation is that the order in which criteria are taken up affects the result; the same relative-importance judgements given in a different order can produce different weights, because every weight is built on top of the one before it. Second, like SWARA, PIPRECIA rests on a single expert's or group's sequence of judgements, and there is no internal-consistency check across these judgements (of the kind AHP's consistency ratio provides). Third, restricting the relative-importance number to the range 0 to 2 can struggle to capture fine gradations where one criterion is far more important than the one before it. Fourth, while PIPRECIA solves SWARA's ranking problem, it introduces its own order-of-treatment problem; this has been criticised as the same underlying difficulty reappearing under a different constraint (Stanujkić et al., 2021).

The most common mistake is interpreting the relative-importance number as in SWARA; in SWARA this number only expresses "how much less important," whereas in PIPRECIA it is read in both directions, above or below 1, so the same figure means opposite things in the two methods. A second mistake is choosing the order of treatment at random and never testing whether that order affects the result; the same judgements should be repeated in a different order and the results compared. A third mistake is choosing the first criterion (the one treated as reference) without justification; that criterion's relative weight is the analysis's starting point. A fourth mistake is reading the last criterion's high or low weight directly as "genuine importance," ignoring that it may be the result of a cumulative calculation.

The governing principle is this:

PIPRECIA's weights are the cumulative result of the consecutive relative-importance judgements given in the order the criteria were taken up; if that order changes, the weights can change too, and the report must show this sensitivity.