Fuzzy SPC (Fuzzy Symmetry Point of Criterion, TFN-component profile)

Fuzzy SPC is not a ranking method; it does not order alternatives, it produces criterion weights. Instead of a single figure in each cell, it takes a triangular fuzzy number (TFN) as input: a lower bound, a most likely value and an upper bound.

The crisp method it rests on, SPC (Symmetry Point of Criterion), was proposed by Gligorić and colleagues in 2023. The idea is to look at the "symmetry point" exactly midway between a criterion's smallest and largest value, and to measure how far the alternatives sit from this point. DecisionMind's fuzzy profile applies this calculation separately, and independently, to each of the TFN's three components, lower bound, most likely value, upper bound, and averages the three results. Classical SPC itself rests on a verifiable source published in a peer-reviewed journal in 2023; but this three-component fuzzy adaptation is not an established method defined in a separate academic paper and known under the name "fuzzy SPC." DecisionMind's manifest describes it as its own engineering profile. Other fuzzy extensions of SPC also exist in the literature, for example modified SPC methods built on spherical fuzzy sets, but these use a different fuzzy framework and are not the same as DecisionMind's three-component approach.

The idea behind SPC is to compare a criterion's "midpoint" with how far the alternatives sit from it. The exact midpoint of a criterion's smallest and largest value is that criterion's symmetry point. The closer an alternative sits to this point, the more "typical" it is; the further away, the more "extreme" a value it carries. SPC builds a "symmetry modulus" by relating a criterion's average distance across all alternatives to each alternative's own value, and converts this modulus into a weight. The method looks for whichever criterion scatters its alternatives most from the symmetry point; it does not look at the criterion's direction (more is better or less is better), only at distance.

The fuzzy adaptation adds this question: how much does the result change when the TFN's three components (pessimistic, most likely, optimistic reading) are put through the same symmetry calculation? Unlike PCA and standard deviation, SPC works on raw values, without first scaling into the range 0 to 1. This means the TFN's three components leave a more independent mark on one another than under PCA or standard deviation; the effect of uncertainty on the weight tends to come out larger here.

The method proceeds through three steps.

First, input validation. Every cell's triangular fuzzy number is checked to satisfy lower bound ≤ most likely value ≤ upper bound, all values are confirmed to be strictly positive (SPC is undefined for zero or negative values), and a direction is confirmed for every criterion. A minimum of two alternatives and two criteria is required.

Second, three independent SPC calculations. For every criterion, the midpoint of its smallest and largest value, that is, its symmetry point, is found. Every alternative's absolute distance to this point is calculated, and these distances are averaged. This average distance is divided by each alternative's own value to obtain a "modulus," and averaging the moduli across alternatives gives the criterion's symmetry modulus. This calculation is applied separately, on raw values (without scaling), to the TFN's lower-bound table, most-likely-value table and upper-bound table.

Third, averaging and an uncertainty measure. The criteria's symmetry moduli are divided by their own sum to obtain a separate weight vector for each component; these three weight vectors are averaged and renormalised to obtain the final weight vector. DecisionMind also computes and reports how far this average sits from the weight derived from the most-likely value alone, and the largest weight difference among the three components.

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

The weight vector reflects, as the average of three fuzzy readings, how far a criterion scatters its alternatives from its own symmetry point. Because SPC works on raw values, the difference among the components here tends to come out larger than under PCA or standard deviation; the width of the TFN tends to affect the weight more markedly in this profile. If the difference among the components is small, the three readings give a similar result; if it is large, the choice of lower and upper bound genuinely changes the result, and the report should state this sensitivity specifically.

The weight measures how far the alternatives sit from the criterion's own midpoint, not the criterion's importance to the decision-maker.

Thus instead of writing:

"The fuzzy SPC analysis showed that this criterion is the most important criterion"

the report should read:

"On the average of these three fuzzy readings, the alternatives scatter most from the symmetry point on this criterion; the difference between the lower and upper bound changes the weight markedly, showing that the effect of uncertainty on the result is large"

This profile works with fuzzy data (triangular fuzzy numbers, TFNs): every cell holds a triple, lower bound, most likely value and upper bound, instead of a single figure. All values must be strictly positive; SPC is undefined for zero or negative values. If your data is crisp, DecisionMind's crisp counterpart of the same idea is the separate card, SPC (Gligorić et al., 2023). This fuzzy profile has no separate extension of its own within DecisionMind.

You need the following: alternatives in rows, criteria in columns, a triple in every cell satisfying l ≤ m ≤ u, all three strictly positive. Criterion direction (more is better or less is better) is requested by the manifest, but SPC's own calculation does not look at this direction; direction is kept only for how the weight is presented. Weights are not entered; the method produces them. A minimum of two alternatives and two criteria is required.

If your criteria are numerical but not exact, given as an interval from expert judgement, and all values are positive, this profile is an option. It is especially suitable if you want a weight measure independent of the choice of normalisation scheme, whether min-max or vector; this is precisely one advantage of classical SPC. Where it particularly matters to see how much uncertainty affects the weight, this profile, working on raw values, shows this effect more markedly than PCA or standard deviation.

The cases where it should not be used follow both from its philosophy and from the nature of its source. If your data contains a zero or negative value, SPC is undefined; the data should first be shifted, or another method chosen. If the result needs to be an academically established "fuzzy SPC" method resting on a single literature source, for example if a SPC extension defined within a spherical or Fermatean fuzzy framework is sought, this profile does not substitute for it; DecisionMind's three-component approach is a separate engineering decision.

Data is fuzzy, positive, a measure independent of the normalisation choice is wanted → Fuzzy SPC

Data is crisp → SPC (Gligorić et al., 2023)

Your data contains a zero or negative value → Shift the data first, or choose another objective method

An academic publication requires a specific SPC extension such as spherical or Fermatean fuzzy → Use the relevant literature source, not this profile

How much the weights are affected by uncertainty does not matter, a single crisp figure is sufficient → Feed the most likely value directly into classical SPC

Classical SPC's, and hence this fuzzy profile's, most important strength is that it does not depend on the choice of normalisation scheme; whereas methods such as TOPSIS or CRITIC first require a scaling form to be chosen, SPC works directly on raw values. Its calculation is simple: it uses only the symmetry point and distance, requiring no correlation or eigenvalue calculation. Because it works on raw values, comparing the three components shows how much the width of the TFN affects the weight more markedly than under PCA or standard deviation.

The most important limitation is the nature of its source. Although classical SPC's founding paper (Gligorić et al., 2023) is a verifiable source, this three-component fuzzy adaptation does not rest on a separate academic paper; it is derived from DecisionMind's own source code, and the manifest flags it as "evidence level C." Second, SPC's inability to work with zero or negative values can cause problems where the TFN's lower bound is small or close to zero. Third, running the three components independently disregards the TFN's internal consistency. Fourth, working on raw values leads this profile to show a larger uncertainty effect than PCA and standard deviation. This is as much a risk as a strength: if the scale of magnitude differs greatly between criteria, for instance if one runs 1-10 and another 1000-10000, the symmetry modulus can behave more sensitively towards the larger-scale criterion. Rani, Chen and Mishra's (2026) modified SPC study, built on spherical fuzzy sets, also shows that there is no single standard way of carrying SPC into different fuzzy frameworks, and that each adaptation carries its own assumptions.

The most common mistake is running this profile without noticing a zero or negative value in the data; SPC is undefined for such a column.

A second mistake is presenting this profile as "the named fuzzy SPC method defined in the literature"; classical SPC has a founding paper, but this three-component fuzzy adaptation is DecisionMind's own engineering decision. A third mistake is placing criteria measured on very different scales, one with small and one with very large numbers, side by side without checking this; because SPC works on raw values, the larger-scale criterion's modulus can come out disproportionate. A fourth mistake is looking only at the final weight and never examining the difference among the three components; in this profile that difference is typically not a size to be dismissed.

The governing principle is this:

The fuzzy SPC weight is the average, across three fuzzy readings, of how far the alternatives scatter from the criterion's symmetry point; the report must show the difference among the components, which is typically large in this profile, and must state that this three-component adaptation is DecisionMind's own engineering profile, kept separate from classical SPC itself.