SPC (Symmetry Point of Criterion method)

SPC is not a ranking method; it does not rank alternatives, it produces weights for criteria. Once you hold a numerical decision table of alternatives and criteria, the method draws a midpoint for every criterion from its own smallest and largest value, and assigns weight by measuring how much the alternatives differ from that point. These weights then become the input to a ranking method such as TOPSIS, VIKOR or SAW.

The method was proposed by Gligorić, Gligorić, Miljanović, Lutovac and Milutinović in 2023; it was developed to determine the criterion weights of a partitioning algorithm in mining. Among objective weighting methods, it is still new, with few applications so far.

SPC's underlying idea is to treat the exact midpoint between a criterion's two extreme values as a fixed reference point. This point is thought of as the criterion's "neutral centre." It then looks at how far every alternative falls from this centre, and these distances are scaled against the alternative's own value. If, on a given criterion, alternatives spread relatively far from the centre, that criterion strongly discriminates between alternatives and receives a high weight.

A consequence of this philosophy is that the method never reads a criterion's direction (higher is better or lower is better). SPC's core equations look only at distance and ratio; they never ask "is larger better or is smaller better." This is a different design choice from Entropy and SD-WEIGHT, and it is both the method's strength and its limitation: because direction information never enters, cost criteria need no separate reversal step, but this also means the method cannot see the distinction between "good" and "bad."

The method proceeds through six steps.

First, checking the inputs. Every value in the decision table is confirmed to be finite and strictly positive. SPC is a ratio-based method and cannot work with a zero or negative value.

Second, the symmetry point. For every criterion, the exact midpoint between the smallest and largest value is taken. This is that criterion's symmetry point, a single number.

Third, distance. For every alternative, the absolute difference between its value on each criterion and that criterion's symmetry point is calculated. This difference comes out small for alternatives close to the symmetry point and large for those far from it.

Fourth, ratio. The average of a criterion's distances across all alternatives is taken, and this average is divided by each alternative's own value. This produces a unitless ratio called the "symmetry modulus."

Fifth, the per-criterion summary. The average is taken of the ratios calculated across all alternatives for a criterion. This single number forms that criterion's symmetry modulus vector.

Sixth, normalisation. The criteria's symmetry moduli are summed, and each is divided by this total to convert it into a weight vector summing to 1.

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

An SPC weight does not show a criterion's importance in the decision-maker's eyes; it shows, proportionally, how far the alternatives in the table at hand spread from that criterion's symmetry point. A high weight does not mean "this criterion is the most important"; it means "in this alternative set, this criterion's values are, proportionally, the most spread out relative to their own centre." Because SPC never reads direction information, the weight never says whether a criterion's spread runs in a "good" or "bad" direction; it only says how large the spread is.

Because SPC is a ratio-based method, a criterion with large numbers (a volume in cubic metres, say) and one with small numbers (a ratio between 0 and 1, say) can receive different weights even with the same absolute spread, because the ratio is calculated by dividing by the alternative's own value. For this reason, the weights are meaningful only with this table's own units of measurement and cannot be compared with another table.

Thus instead of writing:

"The SPC analysis proved that the thickness criterion is the most important criterion"

the report should read:

"In this alternative set, the thickness criterion's values are, proportionally, the most spread out relative to their own symmetry point; the SPC weight reflects this spread, not the decision-maker's order of priority"

SPC works with crisp data and requires every value to be strictly positive; if any cell is zero or negative, the method does not work and the data must first be shifted. Alongside the base method, DecisionMind also records a fuzzy extension (Fuzzy SPC); there are two SPC members in total. The founding paper announced fuzzy SPC only as future work; the fuzzy member in DecisionMind is a separate implementation filling that gap.

You need alternatives in rows, criteria in columns, a strictly positive number in every cell, and no empty cells. Direction information (higher or lower is better) is not needed, because SPC never reads it. No weight is entered; the method produces the weight. A minimum of two alternatives and two criteria is required. If every alternative carries the same value in a column, the symmetry modulus comes out zero and that criterion receives zero weight.

SPC is a suitable choice if your data consists of strictly positive measurements, you do not want to mark criterion direction separately, and a fast, data-derived weight calculation is enough. It is a natural choice particularly in measurement-based fields such as engineering and mining, in problems close to the founding paper's own context.

The situations where it should not be used follow from its philosophy. If you want criterion direction to be reflected in the weight, SPC is unsuitable, because the method never reads direction; this information only comes into play at the ranking stage. If your data contains a zero or negative value, SPC cannot be applied directly. If there is a strong relationship between criteria, SPC does not take this into account.

Data strictly positive, weight should come quickly from the data → SPC

Criterion direction should also affect the weight → SD-WEIGHT or Entropy

The relationship between criteria should also be taken into account → CRITIC

Data contains a zero or negative value → SPC cannot be applied; shift the data first or choose another method

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

SPC's greatest strength is that it works independently of criterion direction; it needs no step to reverse cost criteria, and this removes from the outset any sign errors that step could introduce. Its calculation can be followed step by step; the idea of a symmetry point is easy to explain to a decision-maker. It asks for no external parameter, and the same table gives everyone the same weight.

Its limitations stem from this same design. First, direction-blindness is as much a limitation as a strength: the method never sees, at any step, the difference between "larger is better" and "smaller is better," and a user expecting this distinction to show in the weight can be misled. Second, being ratio-based makes SPC sensitive to scale magnitude; on criteria expressed with very large numbers, the modulus can come out small. Third, like SD-WEIGHT, it does not see the correlation between criteria, and the information in related criteria can be counted twice in the weights (Wang and Luo, 2010, make a similar criticism of standard-deviation-based methods). Fourth, it cannot work with zero or negative data at all; this is a stricter restriction than Entropy or SD-WEIGHT carries. Fifth, the method is still new and the number of independent applications is small; its long-term behaviour has not been tested as widely as Entropy or CRITIC.

The most common mistake is reporting an SPC weight as "importance." The sentence "thickness is the most important criterion" is wrong; the correct statement is that thickness is the criterion that discriminates most between the alternatives.

A second mistake is running SPC without noticing a zero or negative value in the data; in that case the ratio step becomes undefined or produces meaningless numbers. A third is assuming an SPC weight also reflects criterion direction; SPC never reads direction, which only comes into play in the ranking method. A fourth is feeding SPC criteria in different units of measurement without first bringing them onto a common scale; because the ratio is calculated regardless, a result is still produced, but large-scale criteria can end up with an unfairly low weight through a small modulus. A fifth is carrying the weights derived from this table over to a different alternative set.

The governing principle is this:

An SPC weight measures a criterion's proportional spread relative to its symmetry point; it shows spread, not direction, and the report must not conflate the two.