Picture fuzzy CODAS (Simic, Karagoz, Deveci & Aydın, 2021)

Four things change. The decision logic stays the same.

Cells. In crisp CODAS every cell is a single number. Here every cell is three numbers: a degree of yes (μ), a degree of abstention (η) and a degree of no (ν). The three cannot sum to more than 1; the remaining share is the portion left unanswered. Criterion weights are also picture fuzzy triples; the user enters the weight, too, as a judgement in yes-abstention-no form. The method's own literature includes a group step that merges the votes of more than one expert. DecisionMind does not support group decisions in this family. The user enters a single, already-merged vote distribution.

Scale equalisation. Crisp CODAS divides every column by its largest or smallest value. There is no separate division step in the picture fuzzy version; every cell is already a vote between 0 and 1. For cost-direction criteria, the method swaps μ and ν. The yes share given to the statement "this supplier's delay risk is high" swaps places with the rejection share, and the statement is inverted. Every cell is then scaled by the criterion's weight through picture fuzzy multiplication.

Negative-ideal and distance. In crisp CODAS the negative ideal is built from each criterion's single worst number. Here the worst triple is chosen for every criterion: the lowest yes share, the highest abstention share, and the highest no share. DecisionMind holds this combination fixed; the literature has also proposed a different combination (lowest yes, lowest abstention, highest no), which gives a different negative-ideal point. Every alternative's Euclidean distance (E) and taxicab distance (T) to this point are calculated; the difference between the two is that the squares, or the absolute differences, of the three components (yes, abstention, no) are summed separately.

Assessment score. As in crisp CODAS, it is built through pairwise comparisons and can come out positive or negative. The threshold value (τ) is open to the user here too; the source paper gives 0.05 as its default, which differs from crisp CODAS's 0.02.

DecisionMind fixes Cuong's (2013) picture fuzzy operational rules (addition, multiplication) for this family; a different set of operational rules in the literature (Wang 2017/Liang 2018) can give a different weighted matrix, and therefore a different ranking.

The assessment score is read as in crisp CODAS: it is a relative score, coming out negative is not a failure, and the negative ideal shifts when the set of alternatives changes. The difference is here: beneath the score there is now a three-component vote-distribution uncertainty. The score difference between two alternatives does not say whether it comes from the abstention share or from genuine rejection.

Thus instead of writing:

"In picture fuzzy CODAS, the larger the score difference, the more certain the result"

the report should read:

"The score difference is the combined effect of the share on which the board abstained and the share that clearly said no; which of the two dominates should be shown separately in the report"

Use this extension when criterion scores come from a vote, a survey or a spread of opinion, and the abstention share is separately recorded. Converting a measured criterion (price, time) into a yes-abstention-no triple is wrong; this should follow the conversion rule set out on the Picture Fuzzy data-type card. In DecisionMind, the table must be of a single type. Base CODAS's exit condition applies here too: where no concession is acceptable on a criterion, this compensatory family is not the right choice.

Confusing the value-space constraint. The constraint is μ+η+ν ≤ 1. It should not be confused with the intuitionistic fuzzy structure's constraint of μ+ν ≤ 1, or with the Pythagorean structure's constraint of μ²+ν² ≤ 1; these three structures trace out different admissible regions.

Changing the negative-ideal combination without reporting it. DecisionMind uses the combination of lowest yes, highest abstention, highest no. A different combination gives a different negative-ideal point and a different ranking; which one was used should be stated in the report.

Inventing the abstention share after the fact. If the vote offered no abstain option, η is unknown. A share added afterwards on the reasoning "it's probably about ten per cent abstaining" is an assumption, not data.

Reducing to a single degree (the yes share alone) first and then running crisp CODAS. This leaves the abstention and no shares out of the calculation, and artificially inflates or shrinks the difference between alternatives.

The governing principle is this:

Picture fuzzy CODAS exists to carry all three shares of a vote distribution through to the last step; any application that treats a share as derived or added afterwards erases this contribution.