Picture fuzzy ARTASI (Kara, Yalçın, Kaygısız, Simić, Örnek and Pamučar, 2024)

Four things change; the adaptive-range and ideal/anti-ideal-benefit logic does not.

Cells and more than one expert. In classical ARTASI every cell is a single number. Here every cell consists of three degrees: yes (μ), abstain (η), no (ν); the sum of all three cannot exceed 1. A feature of this family is that more than one expert can assess the same cell separately. If there is more than one expert, the experts' triplets are first combined with their own weights; with a single expert, this combination step leaves the triplet unchanged. Quantitative criteria, that is, criteria already measured numerically, are kept apart from this triplet and joined to the same table at a later step.

Early defuzzification. Classical ARTASI already starts from a crisp number. In this family, the picture fuzzy triplet is reduced to a single number by a score function before the adaptive range is even built: the yes degree plus the average of the non-abstain share and the non-no share. This early defuzzification allows all of ARTASI's remaining steps (adaptive range, two-level standardisation, ideal/anti-ideal benefit) to stay exactly identical to classical ARTASI; the only difference is where this single number comes from.

Adaptive range and standardisation. There is no difference at all from classical ARTASI in these steps. Every criterion column is placed into a range extended, from its own maximum and minimum defuzzified value, by a margin that depends on the number of alternatives; this range is then mapped onto a fixed scale (1 to 100 by default).

Ideal/anti-ideal benefit and result. As in classical ARTASI, every alternative's benefit from closeness to the ideal and benefit from distance from the anti-ideal are summed separately and combined with an internal correction parameter. This family has two further parameters: one determines whether weight favours ideality or distance from the anti-ideal, the other determines how these two components are folded together. DecisionMind keeps both at their default values (equally weighted, linear) and states this in the report.

DecisionMind fixes early defuzzification, the adaptive range and the default parameters in this family. Weights are taken from outside, as crisp numbers.

The benefit score is read exactly as in classical ARTASI: it shows this particular set of alternatives' own ideality/anti-ideality balance, it is not a percentage, and it cannot be compared with a different analysis.

The difference is this: an alternative that is clearly the best on one criterion does not see its own score affected even if its advantage on that criterion grows further. The adaptive-range and scaling-to-ideal logic sets the share of the alternative that is best on a criterion at a fixed ceiling for that criterion; however much this alternative widens its advantage, its own share does not change, only the share of the alternatives behind it shrinks. The expectation that "this alternative is much better on this criterion, so its total score should also be much higher" therefore does not hold here.

Thus instead of writing:

"A1 is far better than its rivals on this criterion, so its total score should also be far higher than theirs"

the report should read:

"Because A1 is the best alternative on this criterion, its share already sits at a fixed ceiling; the size of its advantage affects not its own score but only its rivals' share"

This extension is used when an assessment has been gathered as a vote, a survey or a distribution of opinion, and the abstain share is separately measured. It is also suitable when more than one expert's opinion needs to be gathered separately and then combined. If the abstain share would have to be invented afterwards, or a single expert's approximate judgement is all that is available, the caution on the data-type card applies, and the picture fuzzy structure is not needed.

The exit condition is the same as for classical ARTASI. The matrix must be of a single type throughout; if no compromise is acceptable on one criterion, this extension too is compensatory.

Manufacturing a triplet from a single proportion. Writing "55% yes" as (0.55; 0; 0.45) by zeroing out the abstain share erases the structure's contribution; the abstain share must be counted separately.

Expecting a large advantage on one criterion to be reflected proportionally in the score. As explained above, the share of the alternative that is best on a criterion sits at a fixed ceiling; the size of its advantage only changes its rivals' share.

Assuming the adaptive range is fixed. As in classical ARTASI, adding or removing an alternative from the table changes the range, and therefore every score; in this family, early defuzzification does not remove this sensitivity.

Ignoring multi-expert weights. When more than one expert is present, the combination step uses the experts' weights; combining the experts' opinions with a plain average gives a different result and must be reported.

The governing principle is this:

Picture fuzzy ARTASI reduces the yes-abstain-no triplet to a single number through an early score, and applies classical ARTASI's adaptive-range logic unchanged after that; being the best on a criterion corresponds to a fixed share, and what matters is that this share exists, not how large it is.